%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU504^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n002.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 10:44:39 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of formulae : 69 ( 31 unt; 0 typ; 2 def)
% Number of atoms : 390 ( 220 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 759 ( 258 ~; 168 |; 12 &; 296 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 208 ( 4 ^; 186 !; 18 ?; 208 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i > $o ).
thf(tp_sK2_SY28,type,
sK2_SY28: $i ).
thf(tp_sK3_SY31,type,
sK3_SY31: $i > ( $i > $o ) > $i ).
thf(tp_sK4_SY26,type,
sK4_SY26: $i > ( $i > $o ) > $i ).
thf(tp_sK5_SY26,type,
sK5_SY26: $i > ( $i > $o ) > $i ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(1,conjecture,
( exuE1
=> ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(2,negated_conjecture,
( ( exuE1
=> ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY5: $i > $o] :
( ? [SY7: $i] :
( ( SY5 @ SY7 )
& ! [SY8: $i] :
( ( SY5 @ SY8 )
=> ( SY7 = SY8 ) ) )
=> ? [Xx: $i] :
( ( SY5 @ Xx )
& ! [Xy: $i] :
( ( SY5 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ? [Xx: $i] : ( SY0 @ Xx ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,exu,exuE1]) ).
thf(4,plain,
( ( ! [SY5: $i > $o] :
( ? [SY7: $i] :
( ( SY5 @ SY7 )
& ! [SY8: $i] :
( ( SY5 @ SY8 )
=> ( SY7 = SY8 ) ) )
=> ? [Xx: $i] :
( ( SY5 @ Xx )
& ! [Xy: $i] :
( ( SY5 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ? [Xx: $i] : ( SY0 @ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ? [Xx: $i] : ( SY0 @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY5: $i > $o] :
( ? [SY7: $i] :
( ( SY5 @ SY7 )
& ! [SY8: $i] :
( ( SY5 @ SY8 )
=> ( SY7 = SY8 ) ) )
=> ? [Xx: $i] :
( ( SY5 @ Xx )
& ! [Xy: $i] :
( ( SY5 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ? [Xx: $i] : ( SY0 @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,exu,exuE1]) ).
thf(10,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,exu,exuE1]) ).
thf(11,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i > $o] :
( ( ~ ~ ! [SY24: $i] :
~ ~ ( ~ ( SV1 @ SY24 )
| ~ ! [SY25: $i] :
( ~ ( SV1 @ SY25 )
| ( SY24 = SY25 ) ) )
| ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY28 )
| ~ ! [SY29: $i] :
( ~ ( sK1_SX0 @ SY29 )
| ( SY28 = SY29 ) ) )
| ~ ! [SY30: $i] :
~ ( sK1_SX0 @ SY30 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV1: $i > $o] :
( ( ( ~ ~ ! [SY24: $i] :
~ ~ ( ~ ( SV1 @ SY24 )
| ~ ! [SY25: $i] :
( ~ ( SV1 @ SY25 )
| ( SY24 = SY25 ) ) ) )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY28 )
| ~ ! [SY29: $i] :
( ~ ( sK1_SX0 @ SY29 )
| ( SY28 = SY29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SY30: $i] :
~ ( sK1_SX0 @ SY30 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: $i > $o] :
( ( ( ~ ! [SY24: $i] :
~ ~ ( ~ ( SV1 @ SY24 )
| ~ ! [SY25: $i] :
( ~ ( SV1 @ SY25 )
| ( SY24 = SY25 ) ) ) )
= $false )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ! [SY28: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY28 )
| ~ ! [SY29: $i] :
( ~ ( sK1_SX0 @ SY29 )
| ( SY28 = SY29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY30: $i] :
~ ( sK1_SX0 @ SY30 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: $i > $o] :
( ( ( ! [SY24: $i] :
~ ~ ( ~ ( SV1 @ SY24 )
| ~ ! [SY25: $i] :
( ~ ( SV1 @ SY25 )
| ( SY24 = SY25 ) ) ) )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ! [SY28: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY28 )
| ~ ! [SY29: $i] :
( ~ ( sK1_SX0 @ SY29 )
| ( SY28 = SY29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: $i] :
( ( ~ ( sK1_SX0 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ SV3 )
| ~ ! [SY31: $i] :
( ~ ( SV1 @ SY31 )
| ( SV3 = SY31 ) ) ) )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ~ ( ~ ( sK1_SX0 @ sK2_SY28 )
| ~ ! [SY32: $i] :
( ~ ( sK1_SX0 @ SY32 )
| ( sK2_SY28 = SY32 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(25,plain,
! [SV2: $i] :
( ( sK1_SX0 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ~ ( SV1 @ SV3 )
| ~ ! [SY31: $i] :
( ~ ( SV1 @ SY31 )
| ( SV3 = SY31 ) ) ) )
= $false )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( ~ ( sK1_SX0 @ sK2_SY28 )
| ~ ! [SY32: $i] :
( ~ ( sK1_SX0 @ SY32 )
| ( sK2_SY28 = SY32 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 )
| ~ ! [SY31: $i] :
( ~ ( SV1 @ SY31 )
| ( SV3 = SY31 ) ) )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ( sK1_SX0 @ sK2_SY28 )
| ~ ! [SY32: $i] :
( ~ ( sK1_SX0 @ SY32 )
| ( sK2_SY28 = SY32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( ~ ! [SY31: $i] :
( ~ ( SV1 @ SY31 )
| ( SV3 = SY31 ) ) )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(31,plain,
( ( ~ ( sK1_SX0 @ sK2_SY28 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ! [SY32: $i] :
( ~ ( sK1_SX0 @ SY32 )
| ( sK2_SY28 = SY32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( ~ ! [SY31: $i] :
( ~ ( SV1 @ SY31 )
| ( SV3 = SY31 ) ) )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( sK1_SX0 @ sK2_SY28 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
( ( ! [SY32: $i] :
( ~ ( sK1_SX0 @ SY32 )
| ( sK2_SY28 = SY32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ! [SY31: $i] :
( ~ ( SV1 @ SY31 )
| ( SV3 = SY31 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: $i] :
( ( ~ ( sK1_SX0 @ SV4 )
| ( sK2_SY28 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
| ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(39,plain,
! [SV4: $i] :
( ( ( ~ ( sK1_SX0 @ SV4 ) )
= $true )
| ( ( sK2_SY28 = SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV4: $i] :
( ( ( sK1_SX0 @ SV4 )
= $false )
| ( ( sK2_SY28 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ! [SY26: $i] :
~ ~ ( ~ ( SV1 @ SY26 )
| ~ ! [SY27: $i] :
( ~ ( SV1 @ SY27 )
| ( SY26 = SY27 ) ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ ( sK4_SY26 @ SV3 @ SV1 ) )
| ~ ! [SY33: $i] :
( ~ ( SV1 @ SY33 )
| ( ( sK4_SY26 @ SV3 @ SV1 )
= SY33 ) ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(47,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ ( sK5_SY26 @ SV3 @ SV1 ) )
| ~ ! [SY34: $i] :
( ~ ( SV1 @ SY34 )
| ( ( sK5_SY26 @ SV3 @ SV1 )
= SY34 ) ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(48,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK4_SY26 @ SV3 @ SV1 ) )
| ~ ! [SY33: $i] :
( ~ ( SV1 @ SY33 )
| ( ( sK4_SY26 @ SV3 @ SV1 )
= SY33 ) ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(49,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK5_SY26 @ SV3 @ SV1 ) )
| ~ ! [SY34: $i] :
( ~ ( SV1 @ SY34 )
| ( ( sK5_SY26 @ SV3 @ SV1 )
= SY34 ) ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(50,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY26 @ SV3 @ SV1 ) )
| ~ ! [SY33: $i] :
( ~ ( SV1 @ SY33 )
| ( ( sK4_SY26 @ SV3 @ SV1 )
= SY33 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK5_SY26 @ SV3 @ SV1 ) )
| ~ ! [SY34: $i] :
( ~ ( SV1 @ SY34 )
| ( ( sK5_SY26 @ SV3 @ SV1 )
= SY34 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY26 @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(53,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ! [SY33: $i] :
( ~ ( SV1 @ SY33 )
| ( ( sK4_SY26 @ SV3 @ SV1 )
= SY33 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK5_SY26 @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ! [SY34: $i] :
( ~ ( SV1 @ SY34 )
| ( ( sK5_SY26 @ SV3 @ SV1 )
= SY34 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK4_SY26 @ SV3 @ SV1 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(57,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ! [SY33: $i] :
( ~ ( SV1 @ SY33 )
| ( ( sK4_SY26 @ SV3 @ SV1 )
= SY33 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK5_SY26 @ SV3 @ SV1 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ! [SY34: $i] :
( ~ ( SV1 @ SY34 )
| ( ( sK5_SY26 @ SV3 @ SV1 )
= SY34 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV3: $i,SV5: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV5 )
| ( ( sK4_SY26 @ SV3 @ SV1 )
= SV5 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV3: $i,SV6: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV6 )
| ( ( sK5_SY26 @ SV3 @ SV1 )
= SV6 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV3: $i,SV5: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV5 ) )
= $true )
| ( ( ( sK4_SY26 @ SV3 @ SV1 )
= SV5 )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV3: $i,SV6: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV6 ) )
= $true )
| ( ( ( sK5_SY26 @ SV3 @ SV1 )
= SV6 )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV3: $i,SV5: $i,SV1: $i > $o] :
( ( ( SV1 @ SV5 )
= $false )
| ( ( ( sK4_SY26 @ SV3 @ SV1 )
= SV5 )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK3_SY31 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV3: $i,SV6: $i,SV1: $i > $o] :
( ( ( SV1 @ SV6 )
= $false )
| ( ( ( sK5_SY26 @ SV3 @ SV1 )
= SV6 )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_SY31 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,65,64,58,56,42,34]) ).
thf(67,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU504^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.07/0.19 % Computer : n002.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:29:12 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.23
% 0.07/0.23 No.of.Axioms: 0
% 0.07/0.23
% 0.07/0.23 Length.of.Defs: 389
% 0.07/0.23
% 0.07/0.23 Contains.Choice.Funs: false
% 0.07/0.23 .
% 0.07/0.23
% 0.07/0.23 ********************************
% 0.07/0.23 * All subproblems solved! *
% 0.07/0.23 ********************************
% 0.07/0.23 % 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:66,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.23
% 0.07/0.23 %**** Beginning of derivation protocol ****
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 67 ****
% 0.07/0.23 %**** clause counter: 66 ****
% 0.07/0.23
% 0.07/0.23 % 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:66,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------