%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM837+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Wed Oct 7 10:35:20 AM UTC 2026
% Result : Theorem 0.06s 0.24s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 127 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 617 ( 385 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 935 ( 295 ~; 127 |; 0 &; 504 @)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 372 ( 0 ^; 343 !; 29 ?; 372 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_geq,type,
geq: $i > $i > $o ).
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_sK1_SY55,type,
sK1_SY55: $i > $i > $i ).
thf(tp_sK2_SY51,type,
sK2_SY51: $i > $i > $i ).
thf(tp_sK3_SY53,type,
sK3_SY53: $i > $i > $i ).
thf(tp_sK4_SY56,type,
sK4_SY56: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd268,type,
vd268: $i ).
thf(tp_vd269,type,
vd269: $i ).
thf(tp_vd271,type,
vd271: $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(2,axiom,
! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(3,axiom,
! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(4,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(5,axiom,
! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(6,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(7,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(8,axiom,
! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(9,axiom,
! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(20,axiom,
less @ vd268 @ vd269,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(170), 270, 0)') ).
thf(22,conjecture,
? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(171)') ).
thf(23,negated_conjecture,
( ( ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,plain,
( ( ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(26,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(28,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(29,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(30,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(31,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(32,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(33,plain,
( ( less @ vd268 @ vd269 )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(34,plain,
( ( ~ ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(35,plain,
( ( less @ vd268 @ vd269 )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(36,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(37,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(38,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(39,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(40,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(41,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(42,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(43,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(44,plain,
( ( ~ ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(45,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(46,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ! [SX2: $i] :
( ( vplus @ SX2 @ SX0 )
!= ( vplus @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(47,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(48,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( less @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(49,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( greater @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(50,plain,
( ( ~ ~ ! [SX0: $i] :
( vd269
!= ( vplus @ vd268 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(52,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(53,plain,
! [SV1: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ( vplus @ ( vplus @ SV1 @ SY27 ) @ SY28 )
= ( vplus @ SV1 @ ( vplus @ SY27 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(54,plain,
! [SV2: $i] :
( ( ! [SY29: $i] :
( ( SV2 != SY29 )
| ~ ~ ! [SY30: $i] :
( SY29
!= ( vplus @ SV2 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV3: $i] :
( ( ! [SY31: $i] :
( ~ ( ( SV3 != SY31 ) )
| ! [SY32: $i] :
( ( vplus @ SY32 @ SV3 )
!= ( vplus @ SY32 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV4: $i] :
( ( ! [SY33: $i] :
( ( SV4 != SY33 )
| ~ ~ ! [SY34: $i] :
( SV4
!= ( vplus @ SY33 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV5: $i] :
( ( ! [SY35: $i] :
~ ( ~ ( ~ ( less @ SY35 @ SV5 )
| ~ ! [SY36: $i] :
( SV5
!= ( vplus @ SY35 @ SY36 ) ) )
| ~ ( ~ ~ ! [SY37: $i] :
( SV5
!= ( vplus @ SY35 @ SY37 ) )
| ( less @ SY35 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV6: $i] :
( ( ! [SY38: $i] :
~ ( ~ ( ~ ( greater @ SY38 @ SV6 )
| ~ ! [SY39: $i] :
( SY38
!= ( vplus @ SV6 @ SY39 ) ) )
| ~ ( ~ ~ ! [SY40: $i] :
( SY38
!= ( vplus @ SV6 @ SY40 ) )
| ( greater @ SY38 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(59,plain,
( ( ~ ! [SX0: $i] :
( vd269
!= ( vplus @ vd268 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV7: $i] :
( ( ! [SY41: $i] :
( ( SV7 = SY41 )
| ~ ! [SY42: $i] :
( SV7
!= ( vplus @ SY41 @ SY42 ) )
| ~ ! [SY43: $i] :
( SY41
!= ( vplus @ SV7 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV8: $i] :
( ( ! [SY44: $i] :
( ~ ~ ! [SY45: $i] :
( SV8
!= ( vplus @ SY44 @ SY45 ) )
| ~ ~ ! [SY46: $i] :
( SY44
!= ( vplus @ SV8 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV9: $i,SV1: $i] :
( ( ! [SY47: $i] :
( ( vplus @ ( vplus @ SV1 @ SV9 ) @ SY47 )
= ( vplus @ SV1 @ ( vplus @ SV9 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV10: $i,SV2: $i] :
( ( ( SV2 != SV10 )
| ~ ~ ! [SY48: $i] :
( SV10
!= ( vplus @ SV2 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV11: $i,SV3: $i] :
( ( ~ ( ( SV3 != SV11 ) )
| ! [SY49: $i] :
( ( vplus @ SY49 @ SV3 )
!= ( vplus @ SY49 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV12: $i,SV4: $i] :
( ( ( SV4 != SV12 )
| ~ ~ ! [SY50: $i] :
( SV4
!= ( vplus @ SV12 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV5: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( less @ SV13 @ SV5 )
| ~ ! [SY51: $i] :
( SV5
!= ( vplus @ SV13 @ SY51 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
( SV5
!= ( vplus @ SV13 @ SY52 ) )
| ( less @ SV13 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV6: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( greater @ SV14 @ SV6 )
| ~ ! [SY53: $i] :
( SV14
!= ( vplus @ SV6 @ SY53 ) ) )
| ~ ( ~ ~ ! [SY54: $i] :
( SV14
!= ( vplus @ SV6 @ SY54 ) )
| ( greater @ SV14 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(68,plain,
( ( ! [SX0: $i] :
( vd269
!= ( vplus @ vd268 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(69,plain,
! [SV15: $i,SV7: $i] :
( ( ( SV7 = SV15 )
| ~ ! [SY55: $i] :
( SV7
!= ( vplus @ SV15 @ SY55 ) )
| ~ ! [SY56: $i] :
( SV15
!= ( vplus @ SV7 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV16: $i,SV8: $i] :
( ( ~ ~ ! [SY57: $i] :
( SV8
!= ( vplus @ SV16 @ SY57 ) )
| ~ ~ ! [SY58: $i] :
( SV16
!= ( vplus @ SV8 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV17: $i,SV9: $i,SV1: $i] :
( ( ( vplus @ ( vplus @ SV1 @ SV9 ) @ SV17 )
= ( vplus @ SV1 @ ( vplus @ SV9 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV10: $i,SV2: $i] :
( ( ( SV2 != SV10 )
= $true )
| ( ( ~ ~ ! [SY48: $i] :
( SV10
!= ( vplus @ SV2 @ SY48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(73,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV11 ) ) )
= $true )
| ( ( ! [SY49: $i] :
( ( vplus @ SY49 @ SV3 )
!= ( vplus @ SY49 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(74,plain,
! [SV12: $i,SV4: $i] :
( ( ( SV4 != SV12 )
= $true )
| ( ( ~ ~ ! [SY50: $i] :
( SV4
!= ( vplus @ SV12 @ SY50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(75,plain,
! [SV5: $i,SV13: $i] :
( ( ~ ( ~ ( less @ SV13 @ SV5 )
| ~ ! [SY51: $i] :
( SV5
!= ( vplus @ SV13 @ SY51 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
( SV5
!= ( vplus @ SV13 @ SY52 ) )
| ( less @ SV13 @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(76,plain,
! [SV6: $i,SV14: $i] :
( ( ~ ( ~ ( greater @ SV14 @ SV6 )
| ~ ! [SY53: $i] :
( SV14
!= ( vplus @ SV6 @ SY53 ) ) )
| ~ ( ~ ~ ! [SY54: $i] :
( SV14
!= ( vplus @ SV6 @ SY54 ) )
| ( greater @ SV14 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV18: $i] :
( ( vd269
!= ( vplus @ vd268 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV15: $i,SV7: $i] :
( ( ( ( SV7 = SV15 )
| ~ ! [SY55: $i] :
( SV7
!= ( vplus @ SV15 @ SY55 ) ) )
= $true )
| ( ( ~ ! [SY56: $i] :
( SV15
!= ( vplus @ SV7 @ SY56 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV16: $i,SV8: $i] :
( ( ( ~ ~ ! [SY57: $i] :
( SV8
!= ( vplus @ SV16 @ SY57 ) ) )
= $true )
| ( ( ~ ~ ! [SY58: $i] :
( SV16
!= ( vplus @ SV8 @ SY58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV10: $i,SV2: $i] :
( ( ( SV2 = SV10 )
= $false )
| ( ( ~ ~ ! [SY48: $i] :
( SV10
!= ( vplus @ SV2 @ SY48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV11: $i,SV3: $i] :
( ( ( SV3 != SV11 )
= $false )
| ( ( ! [SY49: $i] :
( ( vplus @ SY49 @ SV3 )
!= ( vplus @ SY49 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV12: $i,SV4: $i] :
( ( ( SV4 = SV12 )
= $false )
| ( ( ~ ~ ! [SY50: $i] :
( SV4
!= ( vplus @ SV12 @ SY50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV5: $i,SV13: $i] :
( ( ~ ( ~ ( less @ SV13 @ SV5 )
| ~ ! [SY51: $i] :
( SV5
!= ( vplus @ SV13 @ SY51 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(84,plain,
! [SV13: $i,SV5: $i] :
( ( ~ ( ~ ~ ! [SY52: $i] :
( SV5
!= ( vplus @ SV13 @ SY52 ) )
| ( less @ SV13 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV6: $i,SV14: $i] :
( ( ~ ( ~ ( greater @ SV14 @ SV6 )
| ~ ! [SY53: $i] :
( SV14
!= ( vplus @ SV6 @ SY53 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(86,plain,
! [SV6: $i,SV14: $i] :
( ( ~ ( ~ ~ ! [SY54: $i] :
( SV14
!= ( vplus @ SV6 @ SY54 ) )
| ( greater @ SV14 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(87,plain,
! [SV18: $i] :
( ( vd269
= ( vplus @ vd268 @ SV18 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV15: $i,SV7: $i] :
( ( ( SV7 = SV15 )
= $true )
| ( ( ~ ! [SY55: $i] :
( SV7
!= ( vplus @ SV15 @ SY55 ) ) )
= $true )
| ( ( ~ ! [SY56: $i] :
( SV15
!= ( vplus @ SV7 @ SY56 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV16: $i,SV8: $i] :
( ( ( ~ ! [SY57: $i] :
( SV8
!= ( vplus @ SV16 @ SY57 ) ) )
= $false )
| ( ( ~ ~ ! [SY58: $i] :
( SV16
!= ( vplus @ SV8 @ SY58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV2: $i,SV10: $i] :
( ( ( ~ ! [SY48: $i] :
( SV10
!= ( vplus @ SV2 @ SY48 ) ) )
= $false )
| ( ( SV2 = SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV11: $i,SV3: $i] :
( ( ( SV3 = SV11 )
= $true )
| ( ( ! [SY49: $i] :
( ( vplus @ SY49 @ SV3 )
!= ( vplus @ SY49 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(92,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ! [SY50: $i] :
( SV4
!= ( vplus @ SV12 @ SY50 ) ) )
= $false )
| ( ( SV4 = SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV5: $i,SV13: $i] :
( ( ~ ( less @ SV13 @ SV5 )
| ~ ! [SY51: $i] :
( SV5
!= ( vplus @ SV13 @ SY51 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(94,plain,
! [SV13: $i,SV5: $i] :
( ( ~ ~ ! [SY52: $i] :
( SV5
!= ( vplus @ SV13 @ SY52 ) )
| ( less @ SV13 @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(95,plain,
! [SV6: $i,SV14: $i] :
( ( ~ ( greater @ SV14 @ SV6 )
| ~ ! [SY53: $i] :
( SV14
!= ( vplus @ SV6 @ SY53 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(96,plain,
! [SV6: $i,SV14: $i] :
( ( ~ ~ ! [SY54: $i] :
( SV14
!= ( vplus @ SV6 @ SY54 ) )
| ( greater @ SV14 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(97,plain,
! [SV15: $i,SV7: $i] :
( ( ( ! [SY55: $i] :
( SV7
!= ( vplus @ SV15 @ SY55 ) ) )
= $false )
| ( ( SV7 = SV15 )
= $true )
| ( ( ~ ! [SY56: $i] :
( SV15
!= ( vplus @ SV7 @ SY56 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV16: $i,SV8: $i] :
( ( ( ! [SY57: $i] :
( SV8
!= ( vplus @ SV16 @ SY57 ) ) )
= $true )
| ( ( ~ ~ ! [SY58: $i] :
( SV16
!= ( vplus @ SV8 @ SY58 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(99,plain,
! [SV2: $i,SV10: $i] :
( ( ( ! [SY48: $i] :
( SV10
!= ( vplus @ SV2 @ SY48 ) ) )
= $true )
| ( ( SV2 = SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(100,plain,
! [SV11: $i,SV3: $i,SV19: $i] :
( ( ( ( vplus @ SV19 @ SV3 )
!= ( vplus @ SV19 @ SV11 ) )
= $true )
| ( ( SV3 = SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV12: $i,SV4: $i] :
( ( ( ! [SY50: $i] :
( SV4
!= ( vplus @ SV12 @ SY50 ) ) )
= $true )
| ( ( SV4 = SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(102,plain,
! [SV5: $i,SV13: $i] :
( ( ( ~ ( less @ SV13 @ SV5 ) )
= $true )
| ( ( ~ ! [SY51: $i] :
( SV5
!= ( vplus @ SV13 @ SY51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ~ ! [SY52: $i] :
( SV5
!= ( vplus @ SV13 @ SY52 ) ) )
= $true )
| ( ( less @ SV13 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV6: $i,SV14: $i] :
( ( ( ~ ( greater @ SV14 @ SV6 ) )
= $true )
| ( ( ~ ! [SY53: $i] :
( SV14
!= ( vplus @ SV6 @ SY53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV6: $i,SV14: $i] :
( ( ( ~ ~ ! [SY54: $i] :
( SV14
!= ( vplus @ SV6 @ SY54 ) ) )
= $true )
| ( ( greater @ SV14 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV15: $i,SV7: $i] :
( ( ( SV7
!= ( vplus @ SV15 @ ( sK1_SY55 @ SV15 @ SV7 ) ) )
= $false )
| ( ( SV7 = SV15 )
= $true )
| ( ( ~ ! [SY56: $i] :
( SV15
!= ( vplus @ SV7 @ SY56 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(107,plain,
! [SV20: $i,SV16: $i,SV8: $i] :
( ( ( SV8
!= ( vplus @ SV16 @ SV20 ) )
= $true )
| ( ( ~ ~ ! [SY58: $i] :
( SV16
!= ( vplus @ SV8 @ SY58 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV21: $i,SV2: $i,SV10: $i] :
( ( ( SV10
!= ( vplus @ SV2 @ SV21 ) )
= $true )
| ( ( SV2 = SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV11: $i,SV3: $i,SV19: $i] :
( ( ( ( vplus @ SV19 @ SV3 )
= ( vplus @ SV19 @ SV11 ) )
= $false )
| ( ( SV3 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV22: $i,SV12: $i,SV4: $i] :
( ( ( SV4
!= ( vplus @ SV12 @ SV22 ) )
= $true )
| ( ( SV4 = SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV5: $i,SV13: $i] :
( ( ( less @ SV13 @ SV5 )
= $false )
| ( ( ~ ! [SY51: $i] :
( SV5
!= ( vplus @ SV13 @ SY51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ! [SY52: $i] :
( SV5
!= ( vplus @ SV13 @ SY52 ) ) )
= $false )
| ( ( less @ SV13 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(113,plain,
! [SV6: $i,SV14: $i] :
( ( ( greater @ SV14 @ SV6 )
= $false )
| ( ( ~ ! [SY53: $i] :
( SV14
!= ( vplus @ SV6 @ SY53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(114,plain,
! [SV6: $i,SV14: $i] :
( ( ( ~ ! [SY54: $i] :
( SV14
!= ( vplus @ SV6 @ SY54 ) ) )
= $false )
| ( ( greater @ SV14 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV15: $i,SV7: $i] :
( ( ( SV7
= ( vplus @ SV15 @ ( sK1_SY55 @ SV15 @ SV7 ) ) )
= $true )
| ( ( SV7 = SV15 )
= $true )
| ( ( ~ ! [SY56: $i] :
( SV15
!= ( vplus @ SV7 @ SY56 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(116,plain,
! [SV20: $i,SV16: $i,SV8: $i] :
( ( ( SV8
= ( vplus @ SV16 @ SV20 ) )
= $false )
| ( ( ~ ~ ! [SY58: $i] :
( SV16
!= ( vplus @ SV8 @ SY58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(117,plain,
! [SV21: $i,SV2: $i,SV10: $i] :
( ( ( SV10
= ( vplus @ SV2 @ SV21 ) )
= $false )
| ( ( SV2 = SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(118,plain,
! [SV22: $i,SV12: $i,SV4: $i] :
( ( ( SV4
= ( vplus @ SV12 @ SV22 ) )
= $false )
| ( ( SV4 = SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(119,plain,
! [SV13: $i,SV5: $i] :
( ( ( ! [SY51: $i] :
( SV5
!= ( vplus @ SV13 @ SY51 ) ) )
= $false )
| ( ( less @ SV13 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV13: $i,SV5: $i] :
( ( ( ! [SY52: $i] :
( SV5
!= ( vplus @ SV13 @ SY52 ) ) )
= $true )
| ( ( less @ SV13 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(121,plain,
! [SV6: $i,SV14: $i] :
( ( ( ! [SY53: $i] :
( SV14
!= ( vplus @ SV6 @ SY53 ) ) )
= $false )
| ( ( greater @ SV14 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV6: $i,SV14: $i] :
( ( ( ! [SY54: $i] :
( SV14
!= ( vplus @ SV6 @ SY54 ) ) )
= $true )
| ( ( greater @ SV14 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(123,plain,
! [SV7: $i,SV15: $i] :
( ( ( ! [SY56: $i] :
( SV15
!= ( vplus @ SV7 @ SY56 ) ) )
= $false )
| ( ( SV7 = SV15 )
= $true )
| ( ( SV7
= ( vplus @ SV15 @ ( sK1_SY55 @ SV15 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV20: $i,SV8: $i,SV16: $i] :
( ( ( ~ ! [SY58: $i] :
( SV16
!= ( vplus @ SV8 @ SY58 ) ) )
= $false )
| ( ( SV8
= ( vplus @ SV16 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(125,plain,
! [SV13: $i,SV5: $i] :
( ( ( SV5
!= ( vplus @ SV13 @ ( sK2_SY51 @ SV13 @ SV5 ) ) )
= $false )
| ( ( less @ SV13 @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[119]) ).
thf(126,plain,
! [SV23: $i,SV13: $i,SV5: $i] :
( ( ( SV5
!= ( vplus @ SV13 @ SV23 ) )
= $true )
| ( ( less @ SV13 @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV6: $i,SV14: $i] :
( ( ( SV14
!= ( vplus @ SV6 @ ( sK3_SY53 @ SV6 @ SV14 ) ) )
= $false )
| ( ( greater @ SV14 @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[121]) ).
thf(128,plain,
! [SV24: $i,SV6: $i,SV14: $i] :
( ( ( SV14
!= ( vplus @ SV6 @ SV24 ) )
= $true )
| ( ( greater @ SV14 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV7: $i,SV15: $i] :
( ( ( SV15
!= ( vplus @ SV7 @ ( sK4_SY56 @ SV7 @ SV15 ) ) )
= $false )
| ( ( SV7 = SV15 )
= $true )
| ( ( SV7
= ( vplus @ SV15 @ ( sK1_SY55 @ SV15 @ SV7 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[123]) ).
thf(130,plain,
! [SV20: $i,SV8: $i,SV16: $i] :
( ( ( ! [SY58: $i] :
( SV16
!= ( vplus @ SV8 @ SY58 ) ) )
= $true )
| ( ( SV8
= ( vplus @ SV16 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(131,plain,
! [SV13: $i,SV5: $i] :
( ( ( SV5
= ( vplus @ SV13 @ ( sK2_SY51 @ SV13 @ SV5 ) ) )
= $true )
| ( ( less @ SV13 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(132,plain,
! [SV23: $i,SV13: $i,SV5: $i] :
( ( ( SV5
= ( vplus @ SV13 @ SV23 ) )
= $false )
| ( ( less @ SV13 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV6: $i,SV14: $i] :
( ( ( SV14
= ( vplus @ SV6 @ ( sK3_SY53 @ SV6 @ SV14 ) ) )
= $true )
| ( ( greater @ SV14 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(134,plain,
! [SV24: $i,SV6: $i,SV14: $i] :
( ( ( SV14
= ( vplus @ SV6 @ SV24 ) )
= $false )
| ( ( greater @ SV14 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV7: $i,SV15: $i] :
( ( ( SV15
= ( vplus @ SV7 @ ( sK4_SY56 @ SV7 @ SV15 ) ) )
= $true )
| ( ( SV7 = SV15 )
= $true )
| ( ( SV7
= ( vplus @ SV15 @ ( sK1_SY55 @ SV15 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(136,plain,
! [SV20: $i,SV25: $i,SV8: $i,SV16: $i] :
( ( ( SV16
!= ( vplus @ SV8 @ SV25 ) )
= $true )
| ( ( SV8
= ( vplus @ SV16 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV20: $i,SV25: $i,SV8: $i,SV16: $i] :
( ( ( SV16
= ( vplus @ SV8 @ SV25 ) )
= $false )
| ( ( SV8
= ( vplus @ SV16 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(138,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,137,135,134,133,132,131,118,117,109,87,71]) ).
thf(139,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM837+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n026.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 13:43:17 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.24
% 0.06/0.24 No.of.Axioms: 9
% 0.06/0.24
% 0.06/0.24 Length.of.Defs: 0
% 0.06/0.24
% 0.06/0.24 Contains.Choice.Funs: false
% 0.06/0.24 ...
% 0.06/0.24
% 0.06/0.24 ********************************
% 0.06/0.24 * All subproblems solved! *
% 0.06/0.24 ********************************
% 0.06/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:9,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:138,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.24
% 0.06/0.24 %**** Beginning of derivation protocol ****
% 0.06/0.24 % SZS output start CNFRefutation
% See solution above
% 0.06/0.24
% 0.06/0.24 %**** End of derivation protocol ****
% 0.06/0.24 %**** no. of clauses in derivation: 127 ****
% 0.06/0.24 %**** clause counter: 138 ****
% 0.06/0.24
% 0.06/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:9,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:138,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------