%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV220^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 10:49:46 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 1
% Syntax : Number of formulae : 76 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 523 ( 232 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 757 ( 302 ~; 134 |; 25 &; 281 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 154 ( 16 ^; 119 !; 19 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_f,type,
f: b > a ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_SY9,type,
sK2_SY9: a > $o ).
thf(tp_sK3_SY13,type,
sK3_SY13: b > $o ).
thf(tp_sK4_SY7,type,
sK4_SY7: b ).
thf(tp_sK5_SY20,type,
sK5_SY20: a > b ).
thf(tp_sK6_SY20,type,
sK6_SY20: b > a > b ).
thf(tp_w,type,
w: ( b > $o ) > $o ).
thf(1,conjecture,
! [Xx: a] :
( ? [Xt: b] :
( ! [S: b > $o] :
( ( w @ S )
=> ( S @ Xt ) )
& ( Xx
= ( f @ Xt ) ) )
=> ! [S: a > $o] :
( ? [Xt: b > $o] :
( ( w @ Xt )
& ( S
= ( ^ [Xz: a] :
? [Xt0: b] :
( ( Xt @ Xt0 )
& ( Xz
= ( f @ Xt0 ) ) ) ) ) )
=> ( S @ Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5205_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: a] :
( ? [Xt: b] :
( ! [S: b > $o] :
( ( w @ S )
=> ( S @ Xt ) )
& ( Xx
= ( f @ Xt ) ) )
=> ! [S: a > $o] :
( ? [Xt: b > $o] :
( ( w @ Xt )
& ( S
= ( ^ [Xz: a] :
? [Xt0: b] :
( ( Xt @ Xt0 )
& ( Xz
= ( f @ Xt0 ) ) ) ) ) )
=> ( S @ Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: a] :
( ? [Xt: b] :
( ! [S: b > $o] :
( ( w @ S )
=> ( S @ Xt ) )
& ( Xx
= ( f @ Xt ) ) )
=> ! [S: a > $o] :
( ? [Xt: b > $o] :
( ( w @ Xt )
& ( S
= ( ^ [Xz: a] :
? [Xt0: b] :
( ( Xt @ Xt0 )
& ( Xz
= ( f @ Xt0 ) ) ) ) ) )
=> ( S @ Xx ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [SY7: b] :
( ! [S: b > $o] :
( ( w @ S )
=> ( S @ SY7 ) )
& ( sK1_Xx
= ( f @ SY7 ) ) )
=> ! [SY9: a > $o] :
( ? [Xt: b > $o] :
( ( w @ Xt )
& ( SY9
= ( ^ [Xz: a] :
? [Xt0: b] :
( ( Xt @ Xt0 )
& ( Xz
= ( f @ Xt0 ) ) ) ) ) )
=> ( SY9 @ sK1_Xx ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ? [SY7: b] :
( ! [S: b > $o] :
( ( w @ S )
=> ( S @ SY7 ) )
& ( sK1_Xx
= ( f @ SY7 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY9: a > $o] :
( ? [Xt: b > $o] :
( ( w @ Xt )
& ( SY9
= ( ^ [Xz: a] :
? [Xt0: b] :
( ( Xt @ Xt0 )
& ( Xz
= ( f @ Xt0 ) ) ) ) ) )
=> ( SY9 @ sK1_Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SY9: a > $o] :
( ? [Xt: b > $o] :
( ( w @ Xt )
& ( SY9
= ( ^ [Xz: a] :
? [Xt0: b] :
( ( Xt @ Xt0 )
& ( Xz
= ( f @ Xt0 ) ) ) ) ) )
=> ( SY9 @ sK1_Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( sK2_SY9
= ( ^ [SY16: a] :
? [SY17: b] :
( ( SY16
= ( f @ SY17 ) )
& ( sK3_SY13 @ SY17 ) ) ) )
& ( w @ sK3_SY13 )
& ~ ( sK2_SY9 @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY18: b > $o] :
( ~ ( w @ SY18 )
| ( SY18 @ sK4_SY7 ) )
& ( sK1_Xx
= ( f @ sK4_SY7 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(10,plain,
( ( ! [SY18: b > $o] :
( ~ ( w @ SY18 )
| ( SY18 @ sK4_SY7 ) )
& ( sK1_Xx
= ( f @ sK4_SY7 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ( sK2_SY9
= ( ^ [SY16: a] :
? [SY17: b] :
( ( SY16
= ( f @ SY17 ) )
& ( sK3_SY13 @ SY17 ) ) ) )
& ( w @ sK3_SY13 )
& ~ ( sK2_SY9 @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ( ~ ~ ( ( sK2_SY9
!= ( ^ [SX0: a] :
~ ! [SX1: b] :
~ ~ ( ( SX0
!= ( f @ SX1 ) )
| ~ ( sK3_SY13 @ SX1 ) ) ) )
| ~ ( w @ sK3_SY13 ) )
| ~ ~ ( sK2_SY9 @ sK1_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ( ~ ! [SX0: b > $o] :
( ~ ( w @ SX0 )
| ( SX0 @ sK4_SY7 ) )
| ( sK1_Xx
!= ( f @ sK4_SY7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ~ ( ( sK2_SY9
!= ( ^ [SX0: a] :
~ ! [SX1: b] :
~ ~ ( ( SX0
!= ( f @ SX1 ) )
| ~ ( sK3_SY13 @ SX1 ) ) ) )
| ~ ( w @ sK3_SY13 ) )
| ~ ~ ( sK2_SY9 @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SX0: b > $o] :
( ~ ( w @ SX0 )
| ( SX0 @ sK4_SY7 ) )
| ( sK1_Xx
!= ( f @ sK4_SY7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ( sK2_SY9
!= ( ^ [SX0: a] :
~ ! [SX1: b] :
~ ~ ( ( SX0
!= ( f @ SX1 ) )
| ~ ( sK3_SY13 @ SX1 ) ) ) )
| ~ ( w @ sK3_SY13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( sK2_SY9 @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ! [SX0: b > $o] :
( ~ ( w @ SX0 )
| ( SX0 @ sK4_SY7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( sK1_Xx
!= ( f @ sK4_SY7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ ( ( sK2_SY9
!= ( ^ [SX0: a] :
~ ! [SX1: b] :
~ ~ ( ( SX0
!= ( f @ SX1 ) )
| ~ ( sK3_SY13 @ SX1 ) ) ) )
| ~ ( w @ sK3_SY13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( sK2_SY9 @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ! [SX0: b > $o] :
( ~ ( w @ SX0 )
| ( SX0 @ sK4_SY7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( sK1_Xx
= ( f @ sK4_SY7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ( sK2_SY9
!= ( ^ [SX0: a] :
~ ! [SX1: b] :
~ ~ ( ( SX0
!= ( f @ SX1 ) )
| ~ ( sK3_SY13 @ SX1 ) ) ) )
| ~ ( w @ sK3_SY13 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( sK2_SY9 @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: b > $o] :
( ( ~ ( w @ SV1 )
| ( SV1 @ sK4_SY7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( sK2_SY9
!= ( ^ [SX0: a] :
~ ! [SX1: b] :
~ ~ ( ( SX0
!= ( f @ SX1 ) )
| ~ ( sK3_SY13 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ( w @ sK3_SY13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: b > $o] :
( ( ( ~ ( w @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( sK2_SY9
= ( ^ [SX0: a] :
~ ! [SX1: b] :
~ ~ ( ( SX0
!= ( f @ SX1 ) )
| ~ ( sK3_SY13 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( w @ sK3_SY13 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: b > $o] :
( ( ( w @ SV1 )
= $false )
| ( ( SV1 @ sK4_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ! [SV2: a] :
( ( sK2_SY9 @ SV2 )
= ( ~ ! [SY19: b] :
~ ~ ( ( SV2
!= ( f @ SY19 ) )
| ~ ( sK3_SY13 @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( sK2_SY9
= ( ^ [SX0: a] :
~ ! [SX1: b] :
~ ~ ( ( SX0
!= ( f @ SX1 ) )
| ~ ( sK3_SY13 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: a] :
( ( ( sK2_SY9 @ SV3 )
= ( ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV3: a] :
( ( ~ ( ( sK2_SY9 @ SV3 )
| ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
| ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[35]) ).
thf(37,plain,
! [SV3: a] :
( ( ( sK2_SY9 @ SV3 )
= ( ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV3: a] :
( ( ( ~ ( ( sK2_SY9 @ SV3 )
| ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV3: a] :
( ( ( ( sK2_SY9 @ SV3 )
| ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $false )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV3: a] :
( ( ( sK2_SY9 @ SV3 )
= $false )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(41,plain,
! [SV3: a] :
( ( ( ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $false )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(42,plain,
! [SV3: a] :
( ( ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $false )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV3: a] :
( ( ( ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $true )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(44,plain,
! [SV3: a] :
( ( ( ~ ( sK2_SY9 @ SV3 ) )
= $false )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(45,plain,
! [SV3: a] :
( ( ( ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $false )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV4: b,SV3: a] :
( ( ( ~ ~ ( ( SV3
!= ( f @ SV4 ) )
| ~ ( sK3_SY13 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV3: a] :
( ( ( sK2_SY9 @ SV3 )
= $true )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV3: a] :
( ( ( ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $true )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(49,plain,
! [SV4: b,SV3: a] :
( ( ( ~ ( ( SV3
!= ( f @ SV4 ) )
| ~ ( sK3_SY13 @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV3: a] :
( ( ( ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $false )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV4: b,SV3: a] :
( ( ( ( SV3
!= ( f @ SV4 ) )
| ~ ( sK3_SY13 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(52,plain,
! [SV3: a] :
( ( ( ~ ~ ( ( SV3
!= ( f @ ( sK5_SY20 @ SV3 ) ) )
| ~ ( sK3_SY13 @ ( sK5_SY20 @ SV3 ) ) ) )
= $false )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(53,plain,
! [SV4: b,SV3: a] :
( ( ( SV3
!= ( f @ SV4 ) )
= $true )
| ( ( ~ ( sK3_SY13 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV3: a] :
( ( ( ~ ( ( SV3
!= ( f @ ( sK5_SY20 @ SV3 ) ) )
| ~ ( sK3_SY13 @ ( sK5_SY20 @ SV3 ) ) ) )
= $true )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV4: b,SV3: a] :
( ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( ~ ( sK3_SY13 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV3: a] :
( ( ( ( SV3
!= ( f @ ( sK5_SY20 @ SV3 ) ) )
| ~ ( sK3_SY13 @ ( sK5_SY20 @ SV3 ) ) )
= $false )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV3: a,SV4: b] :
( ( ( sK3_SY13 @ SV4 )
= $false )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV3: a] :
( ( ( SV3
!= ( f @ ( sK5_SY20 @ SV3 ) ) )
= $false )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(59,plain,
! [SV3: a] :
( ( ( ~ ( sK3_SY13 @ ( sK5_SY20 @ SV3 ) ) )
= $false )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(60,plain,
! [SV4: b,SV3: a] :
( ( ( ~ ( sK2_SY9 @ SV3 )
| ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $false )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV3: a] :
( ( ( SV3
= ( f @ ( sK5_SY20 @ SV3 ) ) )
= $true )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV3: a] :
( ( ( sK3_SY13 @ ( sK5_SY20 @ SV3 ) )
= $true )
| ( ( sK2_SY9 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(63,plain,
! [SV4: b,SV3: a] :
( ( ( ~ ( sK2_SY9 @ SV3 ) )
= $false )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV4: b,SV3: a] :
( ( ( ~ ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $false )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV4: b,SV3: a] :
( ( ( sK2_SY9 @ SV3 )
= $true )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(66,plain,
! [SV4: b,SV3: a] :
( ( ( ~ ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $true )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(67,plain,
! [SV4: b,SV3: a] :
( ( ( ! [SY20: b] :
~ ~ ( ( SV3
!= ( f @ SY20 ) )
| ~ ( sK3_SY13 @ SY20 ) ) )
= $false )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(68,plain,
! [SV4: b,SV3: a] :
( ( ( ~ ~ ( ( SV3
!= ( f @ ( sK6_SY20 @ SV4 @ SV3 ) ) )
| ~ ( sK3_SY13 @ ( sK6_SY20 @ SV4 @ SV3 ) ) ) )
= $false )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(69,plain,
! [SV4: b,SV3: a] :
( ( ( ~ ( ( SV3
!= ( f @ ( sK6_SY20 @ SV4 @ SV3 ) ) )
| ~ ( sK3_SY13 @ ( sK6_SY20 @ SV4 @ SV3 ) ) ) )
= $true )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(70,plain,
! [SV4: b,SV3: a] :
( ( ( ( SV3
!= ( f @ ( sK6_SY20 @ SV4 @ SV3 ) ) )
| ~ ( sK3_SY13 @ ( sK6_SY20 @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(71,plain,
! [SV4: b,SV3: a] :
( ( ( SV3
!= ( f @ ( sK6_SY20 @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(72,plain,
! [SV3: a,SV4: b] :
( ( ( ~ ( sK3_SY13 @ ( sK6_SY20 @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(73,plain,
! [SV4: b,SV3: a] :
( ( ( SV3
= ( f @ ( sK6_SY20 @ SV4 @ SV3 ) ) )
= $true )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(74,plain,
! [SV3: a,SV4: b] :
( ( ( sK3_SY13 @ ( sK6_SY20 @ SV4 @ SV3 ) )
= $true )
| ( ( SV3
= ( f @ SV4 ) )
= $false )
| ( ( sK3_SY13 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(75,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,74,73,65,62,61,47,37,34,32,31,25]) ).
thf(76,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV220^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n005.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 15:43:14 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.23
% 0.09/0.23 No.of.Axioms: 0
% 0.09/0.23
% 0.09/0.23 Length.of.Defs: 0
% 0.09/0.23
% 0.09/0.23 Contains.Choice.Funs: false
% 0.09/0.23 .
% 0.09/0.23
% 0.09/0.23 ********************************
% 0.09/0.23 * All subproblems solved! *
% 0.09/0.23 ********************************
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:75,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.23
% 0.09/0.23 %**** Beginning of derivation protocol ****
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23
% 0.09/0.23 %**** End of derivation protocol ****
% 0.09/0.23 %**** no. of clauses in derivation: 76 ****
% 0.09/0.23 %**** clause counter: 75 ****
% 0.09/0.23
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:75,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------