%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN550+1 : TPTP v9.3.1. Released v2.2.0.
% 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 : 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 11:06:45 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 105 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 710 ( 168 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 1415 ( 313 ~; 200 |; 39 &; 833 @)
% ( 3 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 220 ( 0 ^; 199 !; 21 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_initial_world,type,
initial_world: $i ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_reachable,type,
reachable: $i > $i > $o ).
thf(tp_sK1_Y,type,
sK1_Y: $i > $i ).
thf(tp_sK2_W,type,
sK2_W: $i > $i > $i ).
thf(tp_sK3_X,type,
sK3_X: $i ).
thf(tp_sK4_Y,type,
sK4_Y: $i > $i ).
thf(tp_sK5_X,type,
sK5_X: $i ).
thf(tp_sK6_Z,type,
sK6_Z: $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( reachable @ X @ Y )
& ( reachable @ Y @ Z ) )
=> ( reachable @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_reachable) ).
thf(2,axiom,
! [X: $i] : ( reachable @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_reachable) ).
thf(3,conjecture,
( ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ( p @ Y ) ) )
<=> ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ? [Z: $i] :
( ( reachable @ Y @ Z )
& ! [W: $i] :
( ( reachable @ Z @ W )
=> ( p @ W ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(4,negated_conjecture,
( ( ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ( p @ Y ) ) )
<=> ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ? [Z: $i] :
( ( reachable @ Y @ Z )
& ! [W: $i] :
( ( reachable @ Z @ W )
=> ( p @ W ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ( p @ Y ) ) )
<=> ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ? [Z: $i] :
( ( reachable @ Y @ Z )
& ! [W: $i] :
( ( reachable @ Z @ W )
=> ( p @ W ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( reachable @ X @ Y )
& ( reachable @ Y @ Z ) )
=> ( reachable @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [X: $i] : ( reachable @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ( p @ Y ) ) )
=> ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ? [Z: $i] :
( ( reachable @ Y @ Z )
& ! [W: $i] :
( ( reachable @ Z @ W )
=> ( p @ W ) ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(9,plain,
( ( ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ? [Z: $i] :
( ( reachable @ Y @ Z )
& ! [W: $i] :
( ( reachable @ Z @ W )
=> ( p @ W ) ) ) ) )
=> ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ( p @ Y ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(10,plain,
( ( ~ ( ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ( p @ Y ) ) )
=> ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ? [Z: $i] :
( ( reachable @ Y @ Z )
& ! [W: $i] :
( ( reachable @ Z @ W )
=> ( p @ W ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ? [Z: $i] :
( ( reachable @ Y @ Z )
& ! [W: $i] :
( ( reachable @ Z @ W )
=> ( p @ W ) ) ) ) )
=> ? [X: $i] :
( ( reachable @ initial_world @ X )
& ! [Y: $i] :
( ( reachable @ X @ Y )
=> ( p @ Y ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [SY12: $i] :
( ~ ( reachable @ sK3_X @ SY12 )
| ( p @ SY12 ) )
& ( reachable @ initial_world @ sK3_X )
& ! [X: $i] :
( ( ( reachable @ X @ ( sK1_Y @ X ) )
& ! [SY10: $i] :
( ( ( reachable @ SY10 @ ( sK2_W @ SY10 @ X ) )
& ~ ( p @ ( sK2_W @ SY10 @ X ) ) )
| ~ ( reachable @ ( sK1_Y @ X ) @ SY10 ) ) )
| ~ ( reachable @ initial_world @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(13,plain,
( ( ! [SY13: $i] :
( ~ ( reachable @ sK5_X @ SY13 )
| ( ! [SY16: $i] :
( ~ ( reachable @ ( sK6_Z @ SY13 ) @ SY16 )
| ( p @ SY16 ) )
& ( reachable @ SY13 @ ( sK6_Z @ SY13 ) ) ) )
& ( reachable @ initial_world @ sK5_X )
& ! [X: $i] :
( ( ( reachable @ X @ ( sK4_Y @ X ) )
& ~ ( p @ ( sK4_Y @ X ) ) )
| ~ ( reachable @ initial_world @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( reachable @ X @ Y )
| ~ ( reachable @ Y @ Z )
| ( reachable @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(15,plain,
( ( ! [X: $i] : ( reachable @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( reachable @ X @ Y )
| ~ ( reachable @ Y @ Z )
| ( reachable @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SY12: $i] :
( ~ ( reachable @ sK3_X @ SY12 )
| ( p @ SY12 ) )
& ( reachable @ initial_world @ sK3_X )
& ! [X: $i] :
( ( ( reachable @ X @ ( sK1_Y @ X ) )
& ! [SY10: $i] :
( ( ( reachable @ SY10 @ ( sK2_W @ SY10 @ X ) )
& ~ ( p @ ( sK2_W @ SY10 @ X ) ) )
| ~ ( reachable @ ( sK1_Y @ X ) @ SY10 ) ) )
| ~ ( reachable @ initial_world @ X ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK3_X @ SX0 )
| ( p @ SX0 ) )
| ~ ( reachable @ initial_world @ sK3_X ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( reachable @ SX0 @ ( sK1_Y @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( ~ ( reachable @ SX1 @ ( sK2_W @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK2_W @ SX1 @ SX0 ) ) )
| ~ ( reachable @ ( sK1_Y @ SX0 ) @ SX1 ) ) )
| ~ ( reachable @ initial_world @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: $i] :
( ( reachable @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV2: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ~ ( reachable @ SV2 @ SY17 )
| ~ ( reachable @ SY17 @ SY18 )
| ( reachable @ SV2 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK3_X @ SX0 )
| ( p @ SX0 ) )
| ~ ( reachable @ initial_world @ sK3_X ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( reachable @ SX0 @ ( sK1_Y @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( ~ ( reachable @ SX1 @ ( sK2_W @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK2_W @ SX1 @ SX0 ) ) )
| ~ ( reachable @ ( sK1_Y @ SX0 ) @ SX1 ) ) )
| ~ ( reachable @ initial_world @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV3: $i,SV2: $i] :
( ( ! [SY19: $i] :
( ~ ( reachable @ SV2 @ SV3 )
| ~ ( reachable @ SV3 @ SY19 )
| ( reachable @ SV2 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK3_X @ SX0 )
| ( p @ SX0 ) )
| ~ ( reachable @ initial_world @ sK3_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( reachable @ SX0 @ ( sK1_Y @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( ~ ( reachable @ SX1 @ ( sK2_W @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK2_W @ SX1 @ SX0 ) ) )
| ~ ( reachable @ ( sK1_Y @ SX0 ) @ SX1 ) ) )
| ~ ( reachable @ initial_world @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ~ ( reachable @ SV2 @ SV3 )
| ~ ( reachable @ SV3 @ SV4 )
| ( reachable @ SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK3_X @ SX0 )
| ( p @ SX0 ) )
| ~ ( reachable @ initial_world @ sK3_X ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( reachable @ SX0 @ ( sK1_Y @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( ~ ( reachable @ SX1 @ ( sK2_W @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK2_W @ SX1 @ SX0 ) ) )
| ~ ( reachable @ ( sK1_Y @ SX0 ) @ SX1 ) ) )
| ~ ( reachable @ initial_world @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( reachable @ SV2 @ SV3 )
| ~ ( reachable @ SV3 @ SV4 ) )
= $true )
| ( ( reachable @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK3_X @ SX0 )
| ( p @ SX0 ) )
| ~ ( reachable @ initial_world @ sK3_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV5: $i] :
( ( ~ ( ~ ( reachable @ SV5 @ ( sK1_Y @ SV5 ) )
| ~ ! [SY20: $i] :
( ~ ( ~ ( reachable @ SY20 @ ( sK2_W @ SY20 @ SV5 ) )
| ~ ~ ( p @ ( sK2_W @ SY20 @ SV5 ) ) )
| ~ ( reachable @ ( sK1_Y @ SV5 ) @ SY20 ) ) )
| ~ ( reachable @ initial_world @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( reachable @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( reachable @ SV3 @ SV4 ) )
= $true )
| ( ( reachable @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK3_X @ SX0 )
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
( ( ~ ( reachable @ initial_world @ sK3_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( reachable @ SV5 @ ( sK1_Y @ SV5 ) )
| ~ ! [SY20: $i] :
( ~ ( ~ ( reachable @ SY20 @ ( sK2_W @ SY20 @ SV5 ) )
| ~ ~ ( p @ ( sK2_W @ SY20 @ SV5 ) ) )
| ~ ( reachable @ ( sK1_Y @ SV5 ) @ SY20 ) ) ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( reachable @ SV2 @ SV3 )
= $false )
| ( ( ~ ( reachable @ SV3 @ SV4 ) )
= $true )
| ( ( reachable @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
( ( ! [SX0: $i] :
( ~ ( reachable @ sK3_X @ SX0 )
| ( p @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( reachable @ initial_world @ sK3_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV5: $i] :
( ( ( ~ ( reachable @ SV5 @ ( sK1_Y @ SV5 ) )
| ~ ! [SY20: $i] :
( ~ ( ~ ( reachable @ SY20 @ ( sK2_W @ SY20 @ SV5 ) )
| ~ ~ ( p @ ( sK2_W @ SY20 @ SV5 ) ) )
| ~ ( reachable @ ( sK1_Y @ SV5 ) @ SY20 ) ) )
= $false )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV2: $i,SV4: $i,SV3: $i] :
( ( ( reachable @ SV3 @ SV4 )
= $false )
| ( ( reachable @ SV2 @ SV3 )
= $false )
| ( ( reachable @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV6: $i] :
( ( ~ ( reachable @ sK3_X @ SV6 )
| ( p @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV5: $i] :
( ( ( ~ ( reachable @ SV5 @ ( sK1_Y @ SV5 ) ) )
= $false )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV5: $i] :
( ( ( ~ ! [SY20: $i] :
( ~ ( ~ ( reachable @ SY20 @ ( sK2_W @ SY20 @ SV5 ) )
| ~ ~ ( p @ ( sK2_W @ SY20 @ SV5 ) ) )
| ~ ( reachable @ ( sK1_Y @ SV5 ) @ SY20 ) ) )
= $false )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV6: $i] :
( ( ( ~ ( reachable @ sK3_X @ SV6 ) )
= $true )
| ( ( p @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV5: $i] :
( ( ( reachable @ SV5 @ ( sK1_Y @ SV5 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV5: $i] :
( ( ( ! [SY20: $i] :
( ~ ( ~ ( reachable @ SY20 @ ( sK2_W @ SY20 @ SV5 ) )
| ~ ~ ( p @ ( sK2_W @ SY20 @ SV5 ) ) )
| ~ ( reachable @ ( sK1_Y @ SV5 ) @ SY20 ) ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV6: $i] :
( ( ( reachable @ sK3_X @ SV6 )
= $false )
| ( ( p @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV5: $i] :
( ( ( reachable @ initial_world @ SV5 )
= $false )
| ( ( reachable @ SV5 @ ( sK1_Y @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ( ~ ( reachable @ SV7 @ ( sK2_W @ SV7 @ SV5 ) )
| ~ ~ ( p @ ( sK2_W @ SV7 @ SV5 ) ) )
| ~ ( reachable @ ( sK1_Y @ SV5 ) @ SV7 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ( ~ ( reachable @ SV7 @ ( sK2_W @ SV7 @ SV5 ) )
| ~ ~ ( p @ ( sK2_W @ SV7 @ SV5 ) ) ) )
= $true )
| ( ( ~ ( reachable @ ( sK1_Y @ SV5 ) @ SV7 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ( reachable @ SV7 @ ( sK2_W @ SV7 @ SV5 ) )
| ~ ~ ( p @ ( sK2_W @ SV7 @ SV5 ) ) )
= $false )
| ( ( ~ ( reachable @ ( sK1_Y @ SV5 ) @ SV7 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(51,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ( reachable @ SV7 @ ( sK2_W @ SV7 @ SV5 ) ) )
= $false )
| ( ( ~ ( reachable @ ( sK1_Y @ SV5 ) @ SV7 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(52,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ~ ( p @ ( sK2_W @ SV7 @ SV5 ) ) )
= $false )
| ( ( ~ ( reachable @ ( sK1_Y @ SV5 ) @ SV7 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(53,plain,
! [SV5: $i,SV7: $i] :
( ( ( reachable @ SV7 @ ( sK2_W @ SV7 @ SV5 ) )
= $true )
| ( ( ~ ( reachable @ ( sK1_Y @ SV5 ) @ SV7 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(54,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ( p @ ( sK2_W @ SV7 @ SV5 ) ) )
= $true )
| ( ( ~ ( reachable @ ( sK1_Y @ SV5 ) @ SV7 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV7: $i,SV5: $i] :
( ( ( reachable @ ( sK1_Y @ SV5 ) @ SV7 )
= $false )
| ( ( reachable @ SV7 @ ( sK2_W @ SV7 @ SV5 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV5: $i,SV7: $i] :
( ( ( p @ ( sK2_W @ SV7 @ SV5 ) )
= $false )
| ( ( ~ ( reachable @ ( sK1_Y @ SV5 ) @ SV7 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV7: $i,SV5: $i] :
( ( ( reachable @ initial_world @ SV5 )
= $false )
| ( ( reachable @ SV7 @ ( sK2_W @ SV7 @ SV5 ) )
= $true )
| ( ( reachable @ ( sK1_Y @ SV5 ) @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV7: $i,SV5: $i] :
( ( ( reachable @ ( sK1_Y @ SV5 ) @ SV7 )
= $false )
| ( ( p @ ( sK2_W @ SV7 @ SV5 ) )
= $false )
| ( ( ~ ( reachable @ initial_world @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV7: $i,SV5: $i] :
( ( ( reachable @ initial_world @ SV5 )
= $false )
| ( ( p @ ( sK2_W @ SV7 @ SV5 ) )
= $false )
| ( ( reachable @ ( sK1_Y @ SV5 ) @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,59,57,47,46,39,37]) ).
thf(61,plain,
( ( ! [X: $i] : ( reachable @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( reachable @ X @ Y )
| ~ ( reachable @ Y @ Z )
| ( reachable @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(63,plain,
( ( ! [SY13: $i] :
( ~ ( reachable @ sK5_X @ SY13 )
| ( ! [SY16: $i] :
( ~ ( reachable @ ( sK6_Z @ SY13 ) @ SY16 )
| ( p @ SY16 ) )
& ( reachable @ SY13 @ ( sK6_Z @ SY13 ) ) ) )
& ( reachable @ initial_world @ sK5_X )
& ! [X: $i] :
( ( ( reachable @ X @ ( sK4_Y @ X ) )
& ~ ( p @ ( sK4_Y @ X ) ) )
| ~ ( reachable @ initial_world @ X ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(64,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK5_X @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( reachable @ ( sK6_Z @ SX0 ) @ SX1 )
| ( p @ SX1 ) )
| ~ ( reachable @ SX0 @ ( sK6_Z @ SX0 ) ) ) )
| ~ ( reachable @ initial_world @ sK5_X ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( reachable @ SX0 @ ( sK4_Y @ SX0 ) )
| ~ ~ ( p @ ( sK4_Y @ SX0 ) ) )
| ~ ( reachable @ initial_world @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(65,plain,
! [SV8: $i] :
( ( reachable @ SV8 @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV9: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( reachable @ SV9 @ SY21 )
| ~ ( reachable @ SY21 @ SY22 )
| ( reachable @ SV9 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(67,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK5_X @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( reachable @ ( sK6_Z @ SX0 ) @ SX1 )
| ( p @ SX1 ) )
| ~ ( reachable @ SX0 @ ( sK6_Z @ SX0 ) ) ) )
| ~ ( reachable @ initial_world @ sK5_X ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( reachable @ SX0 @ ( sK4_Y @ SX0 ) )
| ~ ~ ( p @ ( sK4_Y @ SX0 ) ) )
| ~ ( reachable @ initial_world @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV10: $i,SV9: $i] :
( ( ! [SY23: $i] :
( ~ ( reachable @ SV9 @ SV10 )
| ~ ( reachable @ SV10 @ SY23 )
| ( reachable @ SV9 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(69,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK5_X @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( reachable @ ( sK6_Z @ SX0 ) @ SX1 )
| ( p @ SX1 ) )
| ~ ( reachable @ SX0 @ ( sK6_Z @ SX0 ) ) ) )
| ~ ( reachable @ initial_world @ sK5_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(70,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( reachable @ SX0 @ ( sK4_Y @ SX0 ) )
| ~ ~ ( p @ ( sK4_Y @ SX0 ) ) )
| ~ ( reachable @ initial_world @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(71,plain,
! [SV11: $i,SV10: $i,SV9: $i] :
( ( ~ ( reachable @ SV9 @ SV10 )
| ~ ( reachable @ SV10 @ SV11 )
| ( reachable @ SV9 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(72,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK5_X @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( reachable @ ( sK6_Z @ SX0 ) @ SX1 )
| ( p @ SX1 ) )
| ~ ( reachable @ SX0 @ ( sK6_Z @ SX0 ) ) ) )
| ~ ( reachable @ initial_world @ sK5_X ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(73,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( reachable @ SX0 @ ( sK4_Y @ SX0 ) )
| ~ ~ ( p @ ( sK4_Y @ SX0 ) ) )
| ~ ( reachable @ initial_world @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV11: $i,SV10: $i,SV9: $i] :
( ( ( ~ ( reachable @ SV9 @ SV10 )
| ~ ( reachable @ SV10 @ SV11 ) )
= $true )
| ( ( reachable @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(75,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK5_X @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( reachable @ ( sK6_Z @ SX0 ) @ SX1 )
| ( p @ SX1 ) )
| ~ ( reachable @ SX0 @ ( sK6_Z @ SX0 ) ) ) )
| ~ ( reachable @ initial_world @ sK5_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(76,plain,
! [SV12: $i] :
( ( ~ ( ~ ( reachable @ SV12 @ ( sK4_Y @ SV12 ) )
| ~ ~ ( p @ ( sK4_Y @ SV12 ) ) )
| ~ ( reachable @ initial_world @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV11: $i,SV10: $i,SV9: $i] :
( ( ( ~ ( reachable @ SV9 @ SV10 ) )
= $true )
| ( ( ~ ( reachable @ SV10 @ SV11 ) )
= $true )
| ( ( reachable @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(78,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reachable @ sK5_X @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( reachable @ ( sK6_Z @ SX0 ) @ SX1 )
| ( p @ SX1 ) )
| ~ ( reachable @ SX0 @ ( sK6_Z @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(79,plain,
( ( ~ ( reachable @ initial_world @ sK5_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(80,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ( reachable @ SV12 @ ( sK4_Y @ SV12 ) )
| ~ ~ ( p @ ( sK4_Y @ SV12 ) ) ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV11: $i,SV10: $i,SV9: $i] :
( ( ( reachable @ SV9 @ SV10 )
= $false )
| ( ( ~ ( reachable @ SV10 @ SV11 ) )
= $true )
| ( ( reachable @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ( reachable @ sK5_X @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( reachable @ ( sK6_Z @ SX0 ) @ SX1 )
| ( p @ SX1 ) )
| ~ ( reachable @ SX0 @ ( sK6_Z @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(83,plain,
( ( reachable @ initial_world @ sK5_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(84,plain,
! [SV12: $i] :
( ( ( ~ ( reachable @ SV12 @ ( sK4_Y @ SV12 ) )
| ~ ~ ( p @ ( sK4_Y @ SV12 ) ) )
= $false )
| ( ( ~ ( reachable @ initial_world @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV9: $i,SV11: $i,SV10: $i] :
( ( ( reachable @ SV10 @ SV11 )
= $false )
| ( ( reachable @ SV9 @ SV10 )
= $false )
| ( ( reachable @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV13: $i] :
( ( ~ ( reachable @ sK5_X @ SV13 )
| ~ ( ~ ! [SY24: $i] :
( ~ ( reachable @ ( sK6_Z @ SV13 ) @ SY24 )
| ( p @ SY24 ) )
| ~ ( reachable @ SV13 @ ( sK6_Z @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV12: $i] :
( ( ( ~ ( reachable @ SV12 @ ( sK4_Y @ SV12 ) ) )
= $false )
| ( ( ~ ( reachable @ initial_world @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(88,plain,
! [SV12: $i] :
( ( ( ~ ~ ( p @ ( sK4_Y @ SV12 ) ) )
= $false )
| ( ( ~ ( reachable @ initial_world @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(89,plain,
! [SV13: $i] :
( ( ( ~ ( reachable @ sK5_X @ SV13 ) )
= $true )
| ( ( ~ ( ~ ! [SY24: $i] :
( ~ ( reachable @ ( sK6_Z @ SV13 ) @ SY24 )
| ( p @ SY24 ) )
| ~ ( reachable @ SV13 @ ( sK6_Z @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV12: $i] :
( ( ( reachable @ SV12 @ ( sK4_Y @ SV12 ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(91,plain,
! [SV12: $i] :
( ( ( ~ ( p @ ( sK4_Y @ SV12 ) ) )
= $true )
| ( ( ~ ( reachable @ initial_world @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(92,plain,
! [SV13: $i] :
( ( ( reachable @ sK5_X @ SV13 )
= $false )
| ( ( ~ ( ~ ! [SY24: $i] :
( ~ ( reachable @ ( sK6_Z @ SV13 ) @ SY24 )
| ( p @ SY24 ) )
| ~ ( reachable @ SV13 @ ( sK6_Z @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(93,plain,
! [SV12: $i] :
( ( ( reachable @ initial_world @ SV12 )
= $false )
| ( ( reachable @ SV12 @ ( sK4_Y @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV12: $i] :
( ( ( p @ ( sK4_Y @ SV12 ) )
= $false )
| ( ( ~ ( reachable @ initial_world @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV13: $i] :
( ( ( ~ ! [SY24: $i] :
( ~ ( reachable @ ( sK6_Z @ SV13 ) @ SY24 )
| ( p @ SY24 ) )
| ~ ( reachable @ SV13 @ ( sK6_Z @ SV13 ) ) )
= $false )
| ( ( reachable @ sK5_X @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(96,plain,
! [SV12: $i] :
( ( ( reachable @ initial_world @ SV12 )
= $false )
| ( ( p @ ( sK4_Y @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(97,plain,
! [SV13: $i] :
( ( ( ~ ! [SY24: $i] :
( ~ ( reachable @ ( sK6_Z @ SV13 ) @ SY24 )
| ( p @ SY24 ) ) )
= $false )
| ( ( reachable @ sK5_X @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(98,plain,
! [SV13: $i] :
( ( ( ~ ( reachable @ SV13 @ ( sK6_Z @ SV13 ) ) )
= $false )
| ( ( reachable @ sK5_X @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(99,plain,
! [SV13: $i] :
( ( ( ! [SY24: $i] :
( ~ ( reachable @ ( sK6_Z @ SV13 ) @ SY24 )
| ( p @ SY24 ) ) )
= $true )
| ( ( reachable @ sK5_X @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(100,plain,
! [SV13: $i] :
( ( ( reachable @ SV13 @ ( sK6_Z @ SV13 ) )
= $true )
| ( ( reachable @ sK5_X @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(101,plain,
! [SV14: $i,SV13: $i] :
( ( ( ~ ( reachable @ ( sK6_Z @ SV13 ) @ SV14 )
| ( p @ SV14 ) )
= $true )
| ( ( reachable @ sK5_X @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(102,plain,
! [SV14: $i,SV13: $i] :
( ( ( ~ ( reachable @ ( sK6_Z @ SV13 ) @ SV14 ) )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( reachable @ sK5_X @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(103,plain,
! [SV14: $i,SV13: $i] :
( ( ( reachable @ ( sK6_Z @ SV13 ) @ SV14 )
= $false )
| ( ( p @ SV14 )
= $true )
| ( ( reachable @ sK5_X @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(104,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,103,100,96,93,85,83]) ).
thf(105,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[104,60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN550+1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n005.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 17:24:44 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 2
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 0
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 ..
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 105 ****
% 0.08/0.25 %**** clause counter: 104 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------