%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV167^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n001.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 10:49:41 AM UTC 2026
% Result : Theorem 0.91s 0.43s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 75 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 428 ( 264 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 515 ( 40 ~; 73 |; 7 &; 378 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 312 ( 312 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-4 aty)
% Number of variables : 339 ( 204 ^; 135 !; 0 ?; 339 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xr,type,
sK1_Xr: a > a > a > a > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: a ).
thf(tp_sK3_SY46,type,
sK3_SY46: a ).
thf(tp_sK4_SY49,type,
sK4_SY49: a ).
thf(tp_sK5_SY51,type,
sK5_SY51: a ).
thf(1,conjecture,
! [Xr: a > a > a > a > $o] :
( ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
( ( Xr
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) )
=> ( Xp = Xq ) )
=> ! [Xx1: a,Xy1: a,Xx2: a,Xy2: a] :
( ( Xr @ Xx1 @ Xy1 @ Xx2 @ Xy2 )
=> ( ( Xx1 = Xx2 )
& ( Xy1 = Xy2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM189_pme) ).
thf(2,negated_conjecture,
( ( ! [Xr: a > a > a > a > $o] :
( ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
( ( Xr
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) )
=> ( Xp = Xq ) )
=> ! [Xx1: a,Xy1: a,Xx2: a,Xy2: a] :
( ( Xr @ Xx1 @ Xy1 @ Xx2 @ Xy2 )
=> ( ( Xx1 = Xx2 )
& ( Xy1 = Xy2 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xr: a > a > a > a > $o] :
( ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
( ( Xr
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) )
=> ( Xp = Xq ) )
=> ! [Xx1: a,Xy1: a,Xx2: a,Xy2: a] :
( ( Xr @ Xx1 @ Xy1 @ Xx2 @ Xy2 )
=> ( ( Xx1 = Xx2 )
& ( Xy1 = Xy2 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY15: ( a > a > a ) > a,SY16: ( a > a > a ) > a] :
( ( sK1_Xr
@ ( SY15
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY15
@ ^ [Xx: a,Xy: a] : Xy )
@ ( SY16
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY16
@ ^ [Xx: a,Xy: a] : Xy ) )
=> ( SY15 = SY16 ) )
=> ! [SY25: a,SY26: a,SY27: a,SY28: a] :
( ( sK1_Xr @ SY25 @ SY26 @ SY27 @ SY28 )
=> ( ( SY25 = SY27 )
& ( SY26 = SY28 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY15: ( a > a > a ) > a,SY16: ( a > a > a ) > a] :
( ( sK1_Xr
@ ( SY15
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY15
@ ^ [Xx: a,Xy: a] : Xy )
@ ( SY16
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY16
@ ^ [Xx: a,Xy: a] : Xy ) )
=> ( SY15 = SY16 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY25: a,SY26: a,SY27: a,SY28: a] :
( ( sK1_Xr @ SY25 @ SY26 @ SY27 @ SY28 )
=> ( ( SY25 = SY27 )
& ( SY26 = SY28 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SY25: a,SY26: a,SY27: a,SY28: a] :
( ( sK1_Xr @ SY25 @ SY26 @ SY27 @ SY28 )
=> ( ( SY25 = SY27 )
& ( SY26 = SY28 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY15: ( a > a > a ) > a,SY16: ( a > a > a ) > a] :
( ( sK1_Xr
@ ( SY15
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY15
@ ^ [Xx: a,Xy: a] : Xy )
@ ( SY16
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY16
@ ^ [Xx: a,Xy: a] : Xy ) )
=> ( SY15 = SY16 ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ~ ! [SY25: a,SY26: a,SY27: a,SY28: a] :
( ( sK1_Xr @ SY25 @ SY26 @ SY27 @ SY28 )
=> ( ( SY25 = SY27 )
& ( SY26 = SY28 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SX0: ( a > a > a ) > a,SX1: ( a > a > a ) > a] :
( ~ ( sK1_Xr
@ ( SX0
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SX0
@ ^ [SX2: a,SX3: a] : SX3 )
@ ( SX1
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SX1
@ ^ [SX2: a,SX3: a] : SX3 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ~ ( sK1_Xr @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: ( a > a > a ) > a] :
( ( ! [SY29: ( a > a > a ) > a] :
( ~ ( sK1_Xr
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX3 )
@ ( SY29
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SY29
@ ^ [SX2: a,SX3: a] : SX3 ) )
| ( SV1 = SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ~ ( sK1_Xr @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: ( a > a > a ) > a,SV1: ( a > a > a ) > a] :
( ( ~ ( sK1_Xr
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX3 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX3 ) )
| ( SV1 = SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SY46: a,SY47: a,SY48: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY46 @ SY47 @ SY48 )
| ~ ( ( sK2_SX0 != SY47 )
| ( SY46 != SY48 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV2: ( a > a > a ) > a,SV1: ( a > a > a ) > a] :
( ( ( ~ ( sK1_Xr
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX3 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX3 ) ) )
= $true )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SY49: a,SY50: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ sK3_SY46 @ SY49 @ SY50 )
| ~ ( ( sK2_SX0 != SY49 )
| ( sK3_SY46 != SY50 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
! [SV2: ( a > a > a ) > a,SV1: ( a > a > a ) > a] :
( ( ( sK1_Xr
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX3 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX3 ) )
= $false )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ! [SY51: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ sK3_SY46 @ sK4_SY49 @ SY51 )
| ~ ( ( sK2_SX0 != sK4_SY49 )
| ( sK3_SY46 != SY51 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(20,plain,
! [SV2: ( a > a > a ) > a,SV1: ( a > a > a ) > a] :
( ( ( ! [SV3: a > a > a] :
( ( SV1 @ SV3 )
= ( SV2 @ SV3 ) ) )
= $true )
| ( ( sK1_Xr
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX3 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX3 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV2: ( a > a > a ) > a,SV1: ( a > a > a ) > a] :
( ( ( SV1 = SV2 )
= $true )
| ( ( sK1_Xr
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX3 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX3 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( sK1_Xr @ sK2_SX0 @ sK3_SY46 @ sK4_SY49 @ sK5_SY51 )
| ~ ( ( sK2_SX0 != sK4_SY49 )
| ( sK3_SY46 != sK5_SY51 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(23,plain,
! [SV2: ( a > a > a ) > a,SV4: a > a > a,SV1: ( a > a > a ) > a] :
( ( ( ( SV1 @ SV4 )
= ( SV2 @ SV4 ) )
= $true )
| ( ( sK1_Xr
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX3 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( sK1_Xr @ sK2_SX0 @ sK3_SY46 @ sK4_SY49 @ sK5_SY51 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ( ( sK2_SX0 != sK4_SY49 )
| ( sK3_SY46 != sK5_SY51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( sK1_Xr @ sK2_SX0 @ sK3_SY46 @ sK4_SY49 @ sK5_SY51 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(27,plain,
( ( ( sK2_SX0 != sK4_SY49 )
| ( sK3_SY46 != sK5_SY51 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(28,plain,
( ( ( sK2_SX0 != sK4_SY49 )
= $true )
| ( ( sK3_SY46 != sK5_SY51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(29,plain,
( ( ( sK2_SX0 = sK4_SY49 )
= $false )
| ( ( sK3_SY46 != sK5_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(30,plain,
( ( ( sK3_SY46 = sK5_SY51 )
= $false )
| ( ( sK2_SX0 = sK4_SY49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV2: ( a > a > a ) > a,SV1: ( a > a > a ) > a,SV5: a > a > a] :
( ( ( sK1_Xr
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV1
@ ^ [SX2: a,SX3: a] : SX3 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX2 )
@ ( SV2
@ ^ [SX2: a,SX3: a] : SX3 ) )
= $false )
| ( ( ( SV1 @ SV5 )
= ( SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[21]) ).
thf(43,plain,
! [SV6: ( a > a > a ) > a,SV7: ( a > a > a ) > a] :
( ( ( SV7 = SV6 )
= $true )
| ( ( sK1_Xr
@ ( SV7
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV7
@ ^ [SX0: a,SX1: a] : SX1 )
@ ( SV6
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV6
@ ^ [SX0: a,SX1: a] : SX1 ) )
= $false ) ),
inference(rename,[status(thm)],[21]) ).
thf(46,plain,
! [SV6: ( a > a > a ) > a,SV7: ( a > a > a ) > a] :
( ( ( ( sK1_Xr
@ ( SV7
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV7
@ ^ [SX0: a,SX1: a] : SX1 )
@ ( SV6
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV6
@ ^ [SX0: a,SX1: a] : SX1 ) )
= ( sK1_Xr @ sK2_SX0 @ sK3_SY46 @ sK4_SY49 @ sK5_SY51 ) )
= $false )
| ( ( SV7 = SV6 )
= $true ) ),
inference(res,[status(thm)],[43,26]) ).
thf(47,plain,
! [SV6: ( a > a > a ) > a,SV7: ( a > a > a ) > a] :
( ( ( ! [SV8: a > a > a] :
( ( SV7 @ SV8 )
= ( SV6 @ SV8 ) ) )
= $true )
| ( ( sK1_Xr
@ ( SV7
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV7
@ ^ [SX0: a,SX1: a] : SX1 )
@ ( SV6
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV6
@ ^ [SX0: a,SX1: a] : SX1 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV6: ( a > a > a ) > a,SV7: ( a > a > a ) > a] :
( ( ( SV7 = SV6 )
= $true )
| ( ( sK1_Xr
@ ( SV7
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV7
@ ^ [SX0: a,SX1: a] : SX1 )
@ ( SV6
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV6
@ ^ [SX0: a,SX1: a] : SX1 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV6: ( a > a > a ) > a,SV9: a > a > a,SV7: ( a > a > a ) > a] :
( ( ( ( SV7 @ SV9 )
= ( SV6 @ SV9 ) )
= $true )
| ( ( sK1_Xr
@ ( SV7
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV7
@ ^ [SX0: a,SX1: a] : SX1 )
@ ( SV6
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV6
@ ^ [SX0: a,SX1: a] : SX1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV60: ( a > a > a ) > a] :
( ( ( ( ^ [SX0: a > a > a] : ( SX0 @ ( SX0 @ sK2_SX0 @ ( SV60 @ SX0 ) ) @ sK3_SY46 ) )
= ( ^ [SX0: a > a > a] : sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extuni,[status(esa)],[46:[bind(SV6,$thf( ^ [SX0: a > a > a] : sK4_SY49 )),bind(SV7,$thf( ^ [SX0: a > a > a] : ( SX0 @ ( SX0 @ sK2_SX0 @ ( SV60 @ SX0 ) ) @ sK3_SY46 ) ))]]) ).
thf(51,plain,
! [SV63: ( a > a > a ) > a] :
( ( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK2_SX0 @ ( SX0 @ ( SV63 @ SX0 ) @ sK3_SY46 ) ) )
= ( ^ [SX0: a > a > a] : sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extuni,[status(esa)],[46:[bind(SV6,$thf( ^ [SX0: a > a > a] : sK4_SY49 )),bind(SV7,$thf( ^ [SX0: a > a > a] : ( SX0 @ sK2_SX0 @ ( SX0 @ ( SV63 @ SX0 ) @ sK3_SY46 ) ) ))]]) ).
thf(52,plain,
( ( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK2_SX0 @ sK3_SY46 ) )
= ( ^ [SX0: a > a > a] : sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extuni,[status(esa)],[46:[bind(SV6,$thf( ^ [SX0: a > a > a] : sK4_SY49 )),bind(SV7,$thf( ^ [SX0: a > a > a] : ( SX0 @ sK2_SX0 @ sK3_SY46 ) ))]]) ).
thf(53,plain,
! [SV20: ( a > a > a ) > a] :
( ( ( ( ^ [SX0: a > a > a] : sK2_SX0 )
= ( ^ [SX0: a > a > a] : ( SX0 @ ( SX0 @ sK4_SY49 @ ( SV20 @ SX0 ) ) @ sK5_SY51 ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extuni,[status(esa)],[46:[bind(SV6,$thf( ^ [SX0: a > a > a] : ( SX0 @ ( SX0 @ sK4_SY49 @ ( SV20 @ SX0 ) ) @ sK5_SY51 ) )),bind(SV7,$thf( ^ [SX0: a > a > a] : sK2_SX0 ))]]) ).
thf(54,plain,
! [SV23: ( a > a > a ) > a] :
( ( ( ( ^ [SX0: a > a > a] : sK2_SX0 )
= ( ^ [SX0: a > a > a] : ( SX0 @ sK4_SY49 @ ( SX0 @ ( SV23 @ SX0 ) @ sK5_SY51 ) ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extuni,[status(esa)],[46:[bind(SV6,$thf( ^ [SX0: a > a > a] : ( SX0 @ sK4_SY49 @ ( SX0 @ ( SV23 @ SX0 ) @ sK5_SY51 ) ) )),bind(SV7,$thf( ^ [SX0: a > a > a] : sK2_SX0 ))]]) ).
thf(55,plain,
( ( ( ( ^ [SX0: a > a > a] : sK2_SX0 )
= ( ^ [SX0: a > a > a] : ( SX0 @ sK4_SY49 @ sK5_SY51 ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extuni,[status(esa)],[46:[bind(SV6,$thf( ^ [SX0: a > a > a] : ( SX0 @ sK4_SY49 @ sK5_SY51 ) )),bind(SV7,$thf( ^ [SX0: a > a > a] : sK2_SX0 ))]]) ).
thf(56,plain,
( ( ( ( ^ [SX0: a > a > a] : sK2_SX0 )
= ( ^ [SX0: a > a > a] : sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extuni,[status(esa)],[46:[bind(SV6,$thf( ^ [SX0: a > a > a] : sK4_SY49 )),bind(SV7,$thf( ^ [SX0: a > a > a] : sK2_SX0 ))]]) ).
thf(57,plain,
( ( ( ! [SV162: a > a > a] : ( sK2_SX0 = sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[56]) ).
thf(58,plain,
( ( ( ( ^ [SX0: a > a > a] : sK2_SX0 )
= ( ^ [SX0: a > a > a] : sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[56]) ).
thf(59,plain,
( ( ( ! [SV163: a > a > a] :
( sK2_SX0
= ( SV163 @ sK4_SY49 @ sK5_SY51 ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[55]) ).
thf(60,plain,
( ( ( ( ^ [SX0: a > a > a] : sK2_SX0 )
= ( ^ [SX0: a > a > a] : ( SX0 @ sK4_SY49 @ sK5_SY51 ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV23: ( a > a > a ) > a] :
( ( ( ! [SV164: a > a > a] :
( sK2_SX0
= ( SV164 @ sK4_SY49 @ ( SV164 @ ( SV23 @ SV164 ) @ sK5_SY51 ) ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV23: ( a > a > a ) > a] :
( ( ( ( ^ [SX0: a > a > a] : sK2_SX0 )
= ( ^ [SX0: a > a > a] : ( SX0 @ sK4_SY49 @ ( SX0 @ ( SV23 @ SX0 ) @ sK5_SY51 ) ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV20: ( a > a > a ) > a] :
( ( ( ! [SV165: a > a > a] :
( sK2_SX0
= ( SV165 @ ( SV165 @ sK4_SY49 @ ( SV20 @ SV165 ) ) @ sK5_SY51 ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV20: ( a > a > a ) > a] :
( ( ( ( ^ [SX0: a > a > a] : sK2_SX0 )
= ( ^ [SX0: a > a > a] : ( SX0 @ ( SX0 @ sK4_SY49 @ ( SV20 @ SX0 ) ) @ sK5_SY51 ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[53]) ).
thf(65,plain,
( ( ( ! [SV166: a > a > a] :
( ( SV166 @ sK2_SX0 @ sK3_SY46 )
= sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[52]) ).
thf(66,plain,
( ( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK2_SX0 @ sK3_SY46 ) )
= ( ^ [SX0: a > a > a] : sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[52]) ).
thf(67,plain,
! [SV63: ( a > a > a ) > a] :
( ( ( ! [SV167: a > a > a] :
( ( SV167 @ sK2_SX0 @ ( SV167 @ ( SV63 @ SV167 ) @ sK3_SY46 ) )
= sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[51]) ).
thf(68,plain,
! [SV63: ( a > a > a ) > a] :
( ( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK2_SX0 @ ( SX0 @ ( SV63 @ SX0 ) @ sK3_SY46 ) ) )
= ( ^ [SX0: a > a > a] : sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[51]) ).
thf(69,plain,
! [SV60: ( a > a > a ) > a] :
( ( ( ! [SV168: a > a > a] :
( ( SV168 @ ( SV168 @ sK2_SX0 @ ( SV60 @ SV168 ) ) @ sK3_SY46 )
= sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[50]) ).
thf(70,plain,
! [SV60: ( a > a > a ) > a] :
( ( ( ( ^ [SX0: a > a > a] : ( SX0 @ ( SX0 @ sK2_SX0 @ ( SV60 @ SX0 ) ) @ sK3_SY46 ) )
= ( ^ [SX0: a > a > a] : sK4_SY49 ) )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[50]) ).
thf(71,plain,
( ( ( sK2_SX0 = sK4_SY49 )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(72,plain,
! [SV170: a > a > a] :
( ( ( sK2_SX0
= ( SV170 @ sK4_SY49 @ sK5_SY51 ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(73,plain,
! [SV23: ( a > a > a ) > a,SV171: a > a > a] :
( ( ( sK2_SX0
= ( SV171 @ sK4_SY49 @ ( SV171 @ ( SV23 @ SV171 ) @ sK5_SY51 ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(74,plain,
! [SV20: ( a > a > a ) > a,SV172: a > a > a] :
( ( ( sK2_SX0
= ( SV172 @ ( SV172 @ sK4_SY49 @ ( SV20 @ SV172 ) ) @ sK5_SY51 ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(75,plain,
! [SV173: a > a > a] :
( ( ( ( SV173 @ sK2_SX0 @ sK3_SY46 )
= sK4_SY49 )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV63: ( a > a > a ) > a,SV174: a > a > a] :
( ( ( ( SV174 @ sK2_SX0 @ ( SV174 @ ( SV63 @ SV174 ) @ sK3_SY46 ) )
= sK4_SY49 )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV60: ( a > a > a ) > a,SV175: a > a > a] :
( ( ( ( SV175 @ ( SV175 @ sK2_SX0 @ ( SV60 @ SV175 ) ) @ sK3_SY46 )
= sK4_SY49 )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV176: ( a > a > a ) > a,SV177: a > a > a,SV178: ( a > a > a ) > a] :
( ( ( ( SV178 @ SV177 )
= ( SV176 @ SV177 ) )
= $true )
| ( ( sK1_Xr
@ ( SV178
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV178
@ ^ [SX0: a,SX1: a] : SX1 )
@ ( SV176
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV176
@ ^ [SX0: a,SX1: a] : SX1 ) )
= $false ) ),
inference(rename,[status(thm)],[23]) ).
thf(83,plain,
! [SV176: ( a > a > a ) > a,SV177: a > a > a,SV178: ( a > a > a ) > a] :
( ( ( ( sK1_Xr
@ ( SV178
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV178
@ ^ [SX0: a,SX1: a] : SX1 )
@ ( SV176
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV176
@ ^ [SX0: a,SX1: a] : SX1 ) )
= ( sK1_Xr @ sK2_SX0 @ sK3_SY46 @ sK4_SY49 @ sK5_SY51 ) )
= $false )
| ( ( ( SV178 @ SV177 )
= ( SV176 @ SV177 ) )
= $true ) ),
inference(res,[status(thm)],[78,26]) ).
thf(84,plain,
! [SV229: ( a > a > a ) > a,SV177: a > a > a] :
( ( ( ( SV177 @ ( SV177 @ sK2_SX0 @ ( SV229 @ SV177 ) ) @ sK3_SY46 )
= sK4_SY49 )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extuni,[status(esa)],[83:[bind(SV176,$thf( ^ [SX0: a > a > a] : sK4_SY49 )),bind(SV178,$thf( ^ [SX0: a > a > a] : ( SX0 @ ( SX0 @ sK2_SX0 @ ( SV229 @ SX0 ) ) @ sK3_SY46 ) ))]]) ).
thf(85,plain,
! [SV232: ( a > a > a ) > a,SV177: a > a > a] :
( ( ( ( SV177 @ sK2_SX0 @ ( SV177 @ ( SV232 @ SV177 ) @ sK3_SY46 ) )
= sK4_SY49 )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extuni,[status(esa)],[83:[bind(SV176,$thf( ^ [SX0: a > a > a] : sK4_SY49 )),bind(SV178,$thf( ^ [SX0: a > a > a] : ( SX0 @ sK2_SX0 @ ( SX0 @ ( SV232 @ SX0 ) @ sK3_SY46 ) ) ))]]) ).
thf(86,plain,
! [SV177: a > a > a] :
( ( ( ( SV177 @ sK2_SX0 @ sK3_SY46 )
= sK4_SY49 )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false ) ),
inference(extuni,[status(esa)],[83:[bind(SV176,$thf( ^ [SX0: a > a > a] : sK4_SY49 )),bind(SV178,$thf( ^ [SX0: a > a > a] : ( SX0 @ sK2_SX0 @ sK3_SY46 ) ))]]) ).
thf(87,plain,
! [SV189: ( a > a > a ) > a,SV177: a > a > a] :
( ( ( sK2_SX0
= ( SV177 @ ( SV177 @ sK4_SY49 @ ( SV189 @ SV177 ) ) @ sK5_SY51 ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extuni,[status(esa)],[83:[bind(SV176,$thf( ^ [SX0: a > a > a] : ( SX0 @ ( SX0 @ sK4_SY49 @ ( SV189 @ SX0 ) ) @ sK5_SY51 ) )),bind(SV178,$thf( ^ [SX0: a > a > a] : sK2_SX0 ))]]) ).
thf(88,plain,
! [SV192: ( a > a > a ) > a,SV177: a > a > a] :
( ( ( sK2_SX0
= ( SV177 @ sK4_SY49 @ ( SV177 @ ( SV192 @ SV177 ) @ sK5_SY51 ) ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extuni,[status(esa)],[83:[bind(SV176,$thf( ^ [SX0: a > a > a] : ( SX0 @ sK4_SY49 @ ( SX0 @ ( SV192 @ SX0 ) @ sK5_SY51 ) ) )),bind(SV178,$thf( ^ [SX0: a > a > a] : sK2_SX0 ))]]) ).
thf(89,plain,
! [SV177: a > a > a] :
( ( ( sK2_SX0
= ( SV177 @ sK4_SY49 @ sK5_SY51 ) )
= $true )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extuni,[status(esa)],[83:[bind(SV176,$thf( ^ [SX0: a > a > a] : ( SX0 @ sK4_SY49 @ sK5_SY51 ) )),bind(SV178,$thf( ^ [SX0: a > a > a] : sK2_SX0 ))]]) ).
thf(90,plain,
( ( ( sK2_SX0 = sK4_SY49 )
= $true )
| ( ( sK4_SY49 = sK5_SY51 )
= $false )
| ( ( sK2_SX0 = sK3_SY46 )
= $false ) ),
inference(extuni,[status(esa)],[83:[bind(SV176,$thf( ^ [SX0: a > a > a] : sK4_SY49 )),bind(SV178,$thf( ^ [SX0: a > a > a] : sK2_SX0 ))]]) ).
thf(98,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,90,89,88,87,86,85,84,78,77,76,75,74,73,72,71,70,68,66,64,62,60,58,49,48,43,32,30]) ).
thf(99,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV167^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n001.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 15:49:30 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.91/0.43
% 0.91/0.43 No.of.Axioms: 0
% 0.91/0.43
% 0.91/0.43 Length.of.Defs: 0
% 0.91/0.43
% 0.91/0.43 Contains.Choice.Funs: false
% 0.91/0.43 ...
% 0.91/0.43
% 0.91/0.43 ********************************
% 0.91/0.43 * All subproblems solved! *
% 0.91/0.43 ********************************
% 0.91/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:98,loop_count:5,foatp_calls:3,translation:fof_full)
% 0.91/0.43
% 0.91/0.43 %**** Beginning of derivation protocol ****
% 0.91/0.43 % SZS output start CNFRefutation
% See solution above
% 0.91/0.43
% 0.91/0.43 %**** End of derivation protocol ****
% 0.91/0.43 %**** no. of clauses in derivation: 75 ****
% 0.91/0.43 %**** clause counter: 98 ****
% 0.91/0.43
% 0.91/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:98,loop_count:5,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------