%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV234+2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n016.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 10:56:28 AM UTC 2026
% Result : Theorem 4.15s 0.91s
% Output : CNFRefutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 136 ( 99 unt; 0 typ; 0 def)
% Number of atoms : 647 ( 201 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1198 ( 112 ~; 135 |; 16 &; 921 @)
% ( 0 <=>; 14 =>; 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 : 17 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 229 ( 0 ^; 229 !; 0 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_data,type,
data: $i ).
thf(tp_enc,type,
enc: $i > $i > $i ).
thf(tp_imp,type,
imp: $i ).
thf(tp_inv,type,
inv: $i > $i ).
thf(tp_k3,type,
k3: $i ).
thf(tp_kek,type,
kek: $i ).
thf(tp_km,type,
km: $i ).
thf(tp_kp,type,
kp: $i > $i ).
thf(tp_pin,type,
pin: $i ).
thf(tp_pp,type,
pp: $i ).
thf(tp_public,type,
public: $i > $o ).
thf(tp_xor,type,
xor: $i > $i > $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
public @ ( enc @ ( xor @ km @ imp ) @ ( xor @ kek @ ( xor @ pin @ data ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge9) ).
thf(2,axiom,
public @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge8) ).
thf(3,axiom,
public @ ( enc @ ( xor @ km @ ( kp @ imp ) ) @ ( xor @ kek @ k3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge7) ).
thf(4,axiom,
public @ k3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge6) ).
thf(5,axiom,
public @ ( enc @ ( xor @ kek @ pin ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge5) ).
thf(6,axiom,
public @ pin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge4) ).
thf(7,axiom,
public @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge3) ).
thf(8,axiom,
public @ data,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge2) ).
thf(9,axiom,
public @ imp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge1) ).
thf(10,axiom,
! [U: $i,V: $i,W: $i] :
( ( xor @ U @ z )
= U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_zero) ).
thf(11,axiom,
! [U: $i,V: $i,W: $i] :
( ( xor @ U @ U )
= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_self_cancel) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i] :
( ( xor @ U @ ( xor @ V @ W ) )
= ( xor @ ( xor @ U @ V ) @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_assosciative) ).
thf(13,axiom,
! [U: $i,V: $i,W: $i] :
( ( xor @ U @ V )
= ( xor @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutes) ).
thf(14,axiom,
! [U: $i,V: $i,W: $i] :
( ( enc @ U @ ( enc @ ( inv @ U ) @ V ) )
= V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_decrypt_cancel) ).
thf(15,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( public @ ( kp @ V ) )
& ( public @ W )
& ( public @ ( enc @ ( xor @ km @ ( kp @ V ) ) @ U ) ) )
=> ( public @ ( enc @ ( xor @ km @ V ) @ ( xor @ U @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_part_import_cmd) ).
thf(16,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( public @ V )
& ( public @ ( enc @ ( xor @ U @ V ) @ W ) )
& ( public @ ( enc @ ( xor @ km @ imp ) @ U ) ) )
=> ( public @ ( enc @ ( xor @ km @ V ) @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_import_cmd) ).
thf(17,axiom,
! [U: $i,V: $i] :
( ( ( public @ U )
& ( public @ V ) )
=> ( public @ ( enc @ ( enc @ ( inv @ ( xor @ data @ km ) ) @ U ) @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_data_cmd) ).
thf(18,axiom,
! [U: $i,V: $i] :
( ( ( public @ U )
& ( public @ V ) )
=> ( public @ ( enc @ ( inv @ U ) @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ability_to_decrypt) ).
thf(19,axiom,
! [U: $i,V: $i] :
( ( ( public @ U )
& ( public @ V ) )
=> ( public @ ( enc @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ability_to_encrypt) ).
thf(20,axiom,
! [U: $i] :
( ( public @ U )
=> ( public @ ( kp @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kp_set) ).
thf(21,axiom,
! [U: $i,V: $i] :
( ( ( public @ U )
& ( public @ V ) )
=> ( public @ ( xor @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ability_to_xor) ).
thf(22,conjecture,
public @ ( enc @ pp @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(23,negated_conjecture,
( ( public @ ( enc @ pp @ a ) )
= $false ),
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,plain,
( ( public @ ( enc @ pp @ a ) )
= $false ),
inference(unfold_def,[status(thm)],[23]) ).
thf(25,plain,
( ( public @ ( enc @ ( xor @ km @ imp ) @ ( xor @ kek @ ( xor @ pin @ data ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(26,plain,
( ( public @ a )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(27,plain,
( ( public @ ( enc @ ( xor @ km @ ( kp @ imp ) ) @ ( xor @ kek @ k3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(28,plain,
( ( public @ k3 )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(29,plain,
( ( public @ ( enc @ ( xor @ kek @ pin ) @ pp ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(30,plain,
( ( public @ pin )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,plain,
( ( public @ z )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(32,plain,
( ( public @ data )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(33,plain,
( ( public @ imp )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(34,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( xor @ U @ z )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( xor @ U @ U )
= z ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(36,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( xor @ U @ ( xor @ V @ W ) )
= ( xor @ ( xor @ U @ V ) @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( xor @ U @ V )
= ( xor @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( enc @ U @ ( enc @ ( inv @ U ) @ V ) )
= V ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( public @ ( kp @ V ) )
& ( public @ W )
& ( public @ ( enc @ ( xor @ km @ ( kp @ V ) ) @ U ) ) )
=> ( public @ ( enc @ ( xor @ km @ V ) @ ( xor @ U @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( public @ V )
& ( public @ ( enc @ ( xor @ U @ V ) @ W ) )
& ( public @ ( enc @ ( xor @ km @ imp ) @ U ) ) )
=> ( public @ ( enc @ ( xor @ km @ V ) @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [U: $i,V: $i] :
( ( ( public @ U )
& ( public @ V ) )
=> ( public @ ( enc @ ( enc @ ( inv @ ( xor @ data @ km ) ) @ U ) @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [U: $i,V: $i] :
( ( ( public @ U )
& ( public @ V ) )
=> ( public @ ( enc @ ( inv @ U ) @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [U: $i,V: $i] :
( ( ( public @ U )
& ( public @ V ) )
=> ( public @ ( enc @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [U: $i] :
( ( public @ U )
=> ( public @ ( kp @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ! [U: $i,V: $i] :
( ( ( public @ U )
& ( public @ V ) )
=> ( public @ ( xor @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(46,plain,
( ( ~ ( public @ ( enc @ pp @ a ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,plain,
( ( ! [U: $i] :
( ( xor @ U @ z )
= U ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(48,plain,
( ( ! [U: $i] :
( ( xor @ U @ U )
= z ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(49,plain,
( ( ! [U: $i,V: $i] :
( ( xor @ U @ V )
= ( xor @ V @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(50,plain,
( ( ! [U: $i,V: $i] :
( ( enc @ U @ ( enc @ ( inv @ U ) @ V ) )
= V ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(51,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( public @ ( kp @ V ) )
| ~ ( public @ W )
| ~ ( public @ ( enc @ ( xor @ km @ ( kp @ V ) ) @ U ) )
| ( public @ ( enc @ ( xor @ km @ V ) @ ( xor @ U @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(52,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( public @ V )
| ~ ( public @ ( enc @ ( xor @ U @ V ) @ W ) )
| ~ ( public @ ( enc @ ( xor @ km @ imp ) @ U ) )
| ( public @ ( enc @ ( xor @ km @ V ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(53,plain,
( ( ! [U: $i,V: $i] :
( ~ ( public @ U )
| ~ ( public @ V )
| ( public @ ( enc @ ( enc @ ( inv @ ( xor @ data @ km ) ) @ U ) @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(54,plain,
( ( ! [U: $i,V: $i] :
( ~ ( public @ U )
| ~ ( public @ V )
| ( public @ ( enc @ ( inv @ U ) @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(55,plain,
( ( ! [U: $i,V: $i] :
( ~ ( public @ U )
| ~ ( public @ V )
| ( public @ ( enc @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(56,plain,
( ( ! [U: $i] :
( ~ ( public @ U )
| ( public @ ( kp @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(57,plain,
( ( ! [U: $i,V: $i] :
( ~ ( public @ U )
| ~ ( public @ V )
| ( public @ ( xor @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(58,plain,
( ( ! [U: $i,V: $i] :
( ~ ( public @ U )
| ~ ( public @ V )
| ( public @ ( xor @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(59,plain,
( ( ! [U: $i] :
( ~ ( public @ U )
| ( public @ ( kp @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(60,plain,
( ( ! [U: $i,V: $i] :
( ~ ( public @ U )
| ~ ( public @ V )
| ( public @ ( enc @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(61,plain,
( ( ! [U: $i,V: $i] :
( ~ ( public @ U )
| ~ ( public @ V )
| ( public @ ( enc @ ( inv @ U ) @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(62,plain,
( ( ! [U: $i,V: $i] :
( ~ ( public @ U )
| ~ ( public @ V )
| ( public @ ( enc @ ( enc @ ( inv @ ( xor @ data @ km ) ) @ U ) @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(63,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( public @ V )
| ~ ( public @ ( enc @ ( xor @ U @ V ) @ W ) )
| ~ ( public @ ( enc @ ( xor @ km @ imp ) @ U ) )
| ( public @ ( enc @ ( xor @ km @ V ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(64,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( public @ ( kp @ V ) )
| ~ ( public @ W )
| ~ ( public @ ( enc @ ( xor @ km @ ( kp @ V ) ) @ U ) )
| ( public @ ( enc @ ( xor @ km @ V ) @ ( xor @ U @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(65,plain,
( ( ! [U: $i,V: $i] :
( ( enc @ U @ ( enc @ ( inv @ U ) @ V ) )
= V ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(66,plain,
( ( ! [U: $i,V: $i] :
( ( xor @ U @ V )
= ( xor @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(67,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( xor @ U @ ( xor @ V @ W ) )
= ( xor @ ( xor @ U @ V ) @ W ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(68,plain,
( ( ! [U: $i] :
( ( xor @ U @ U )
= z ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(69,plain,
( ( ! [U: $i] :
( ( xor @ U @ z )
= U ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(70,plain,
( ( public @ imp )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(71,plain,
( ( public @ data )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(72,plain,
( ( public @ z )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(73,plain,
( ( public @ pin )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(74,plain,
( ( public @ ( enc @ ( xor @ kek @ pin ) @ pp ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(75,plain,
( ( public @ k3 )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(76,plain,
( ( public @ ( enc @ ( xor @ km @ ( kp @ imp ) ) @ ( xor @ kek @ k3 ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(77,plain,
( ( public @ a )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(78,plain,
( ( public @ ( enc @ ( xor @ km @ imp ) @ ( xor @ kek @ ( xor @ pin @ data ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(79,plain,
( ( ~ ( public @ ( enc @ pp @ a ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(80,plain,
! [SV1: $i] :
( ( ! [SY30: $i] :
( ~ ( public @ SV1 )
| ~ ( public @ SY30 )
| ( public @ ( xor @ SV1 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(81,plain,
! [SV2: $i] :
( ( ~ ( public @ SV2 )
| ( public @ ( kp @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(82,plain,
! [SV3: $i] :
( ( ! [SY31: $i] :
( ~ ( public @ SV3 )
| ~ ( public @ SY31 )
| ( public @ ( enc @ SV3 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(83,plain,
! [SV4: $i] :
( ( ! [SY32: $i] :
( ~ ( public @ SV4 )
| ~ ( public @ SY32 )
| ( public @ ( enc @ ( inv @ SV4 ) @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(84,plain,
! [SV5: $i] :
( ( ! [SY33: $i] :
( ~ ( public @ SV5 )
| ~ ( public @ SY33 )
| ( public @ ( enc @ ( enc @ ( inv @ ( xor @ data @ km ) ) @ SV5 ) @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(85,plain,
! [SV6: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( public @ SY34 )
| ~ ( public @ ( enc @ ( xor @ SV6 @ SY34 ) @ SY35 ) )
| ~ ( public @ ( enc @ ( xor @ km @ imp ) @ SV6 ) )
| ( public @ ( enc @ ( xor @ km @ SY34 ) @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(86,plain,
! [SV7: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ( public @ ( kp @ SY36 ) )
| ~ ( public @ SY37 )
| ~ ( public @ ( enc @ ( xor @ km @ ( kp @ SY36 ) ) @ SV7 ) )
| ( public @ ( enc @ ( xor @ km @ SY36 ) @ ( xor @ SV7 @ SY37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(87,plain,
! [SV8: $i] :
( ( ! [SY38: $i] :
( ( enc @ SV8 @ ( enc @ ( inv @ SV8 ) @ SY38 ) )
= SY38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(88,plain,
! [SV9: $i] :
( ( ! [SY39: $i] :
( ( xor @ SV9 @ SY39 )
= ( xor @ SY39 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(89,plain,
! [SV10: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ( xor @ SV10 @ ( xor @ SY40 @ SY41 ) )
= ( xor @ ( xor @ SV10 @ SY40 ) @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(90,plain,
! [SV11: $i] :
( ( ( xor @ SV11 @ SV11 )
= z )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(91,plain,
! [SV12: $i] :
( ( ( xor @ SV12 @ z )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(92,plain,
( ( public @ ( enc @ pp @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(93,plain,
! [SV13: $i,SV1: $i] :
( ( ~ ( public @ SV1 )
| ~ ( public @ SV13 )
| ( public @ ( xor @ SV1 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(94,plain,
! [SV2: $i] :
( ( ( ~ ( public @ SV2 ) )
= $true )
| ( ( public @ ( kp @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(95,plain,
! [SV14: $i,SV3: $i] :
( ( ~ ( public @ SV3 )
| ~ ( public @ SV14 )
| ( public @ ( enc @ SV3 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(96,plain,
! [SV15: $i,SV4: $i] :
( ( ~ ( public @ SV4 )
| ~ ( public @ SV15 )
| ( public @ ( enc @ ( inv @ SV4 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(97,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( public @ SV5 )
| ~ ( public @ SV16 )
| ( public @ ( enc @ ( enc @ ( inv @ ( xor @ data @ km ) ) @ SV5 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(98,plain,
! [SV6: $i,SV17: $i] :
( ( ! [SY42: $i] :
( ~ ( public @ SV17 )
| ~ ( public @ ( enc @ ( xor @ SV6 @ SV17 ) @ SY42 ) )
| ~ ( public @ ( enc @ ( xor @ km @ imp ) @ SV6 ) )
| ( public @ ( enc @ ( xor @ km @ SV17 ) @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV7: $i,SV18: $i] :
( ( ! [SY43: $i] :
( ~ ( public @ ( kp @ SV18 ) )
| ~ ( public @ SY43 )
| ~ ( public @ ( enc @ ( xor @ km @ ( kp @ SV18 ) ) @ SV7 ) )
| ( public @ ( enc @ ( xor @ km @ SV18 ) @ ( xor @ SV7 @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV19: $i,SV8: $i] :
( ( ( enc @ SV8 @ ( enc @ ( inv @ SV8 ) @ SV19 ) )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV20: $i,SV9: $i] :
( ( ( xor @ SV9 @ SV20 )
= ( xor @ SV20 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(102,plain,
! [SV21: $i,SV10: $i] :
( ( ! [SY44: $i] :
( ( xor @ SV10 @ ( xor @ SV21 @ SY44 ) )
= ( xor @ ( xor @ SV10 @ SV21 ) @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV13: $i,SV1: $i] :
( ( ( ~ ( public @ SV1 )
| ~ ( public @ SV13 ) )
= $true )
| ( ( public @ ( xor @ SV1 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(104,plain,
! [SV2: $i] :
( ( ( public @ SV2 )
= $false )
| ( ( public @ ( kp @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(105,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ( public @ SV3 )
| ~ ( public @ SV14 ) )
= $true )
| ( ( public @ ( enc @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(106,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( public @ SV4 )
| ~ ( public @ SV15 ) )
= $true )
| ( ( public @ ( enc @ ( inv @ SV4 ) @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(107,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( public @ SV5 )
| ~ ( public @ SV16 ) )
= $true )
| ( ( public @ ( enc @ ( enc @ ( inv @ ( xor @ data @ km ) ) @ SV5 ) @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV22: $i,SV6: $i,SV17: $i] :
( ( ~ ( public @ SV17 )
| ~ ( public @ ( enc @ ( xor @ SV6 @ SV17 ) @ SV22 ) )
| ~ ( public @ ( enc @ ( xor @ km @ imp ) @ SV6 ) )
| ( public @ ( enc @ ( xor @ km @ SV17 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV7: $i,SV23: $i,SV18: $i] :
( ( ~ ( public @ ( kp @ SV18 ) )
| ~ ( public @ SV23 )
| ~ ( public @ ( enc @ ( xor @ km @ ( kp @ SV18 ) ) @ SV7 ) )
| ( public @ ( enc @ ( xor @ km @ SV18 ) @ ( xor @ SV7 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV24: $i,SV21: $i,SV10: $i] :
( ( ( xor @ SV10 @ ( xor @ SV21 @ SV24 ) )
= ( xor @ ( xor @ SV10 @ SV21 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV13: $i,SV1: $i] :
( ( ( ~ ( public @ SV1 ) )
= $true )
| ( ( ~ ( public @ SV13 ) )
= $true )
| ( ( public @ ( xor @ SV1 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ( public @ SV3 ) )
= $true )
| ( ( ~ ( public @ SV14 ) )
= $true )
| ( ( public @ ( enc @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(113,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( public @ SV4 ) )
= $true )
| ( ( ~ ( public @ SV15 ) )
= $true )
| ( ( public @ ( enc @ ( inv @ SV4 ) @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( public @ SV5 ) )
= $true )
| ( ( ~ ( public @ SV16 ) )
= $true )
| ( ( public @ ( enc @ ( enc @ ( inv @ ( xor @ data @ km ) ) @ SV5 ) @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(115,plain,
! [SV22: $i,SV6: $i,SV17: $i] :
( ( ( ~ ( public @ SV17 )
| ~ ( public @ ( enc @ ( xor @ SV6 @ SV17 ) @ SV22 ) )
| ~ ( public @ ( enc @ ( xor @ km @ imp ) @ SV6 ) ) )
= $true )
| ( ( public @ ( enc @ ( xor @ km @ SV17 ) @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV7: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( public @ ( kp @ SV18 ) )
| ~ ( public @ SV23 )
| ~ ( public @ ( enc @ ( xor @ km @ ( kp @ SV18 ) ) @ SV7 ) ) )
= $true )
| ( ( public @ ( enc @ ( xor @ km @ SV18 ) @ ( xor @ SV7 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV13: $i,SV1: $i] :
( ( ( public @ SV1 )
= $false )
| ( ( ~ ( public @ SV13 ) )
= $true )
| ( ( public @ ( xor @ SV1 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(118,plain,
! [SV14: $i,SV3: $i] :
( ( ( public @ SV3 )
= $false )
| ( ( ~ ( public @ SV14 ) )
= $true )
| ( ( public @ ( enc @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(119,plain,
! [SV15: $i,SV4: $i] :
( ( ( public @ SV4 )
= $false )
| ( ( ~ ( public @ SV15 ) )
= $true )
| ( ( public @ ( enc @ ( inv @ SV4 ) @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(120,plain,
! [SV16: $i,SV5: $i] :
( ( ( public @ SV5 )
= $false )
| ( ( ~ ( public @ SV16 ) )
= $true )
| ( ( public @ ( enc @ ( enc @ ( inv @ ( xor @ data @ km ) ) @ SV5 ) @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(121,plain,
! [SV22: $i,SV6: $i,SV17: $i] :
( ( ( ~ ( public @ SV17 )
| ~ ( public @ ( enc @ ( xor @ SV6 @ SV17 ) @ SV22 ) ) )
= $true )
| ( ( ~ ( public @ ( enc @ ( xor @ km @ imp ) @ SV6 ) ) )
= $true )
| ( ( public @ ( enc @ ( xor @ km @ SV17 ) @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(122,plain,
! [SV7: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( public @ ( kp @ SV18 ) )
| ~ ( public @ SV23 ) )
= $true )
| ( ( ~ ( public @ ( enc @ ( xor @ km @ ( kp @ SV18 ) ) @ SV7 ) ) )
= $true )
| ( ( public @ ( enc @ ( xor @ km @ SV18 ) @ ( xor @ SV7 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(123,plain,
! [SV1: $i,SV13: $i] :
( ( ( public @ SV13 )
= $false )
| ( ( public @ SV1 )
= $false )
| ( ( public @ ( xor @ SV1 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(124,plain,
! [SV3: $i,SV14: $i] :
( ( ( public @ SV14 )
= $false )
| ( ( public @ SV3 )
= $false )
| ( ( public @ ( enc @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(125,plain,
! [SV4: $i,SV15: $i] :
( ( ( public @ SV15 )
= $false )
| ( ( public @ SV4 )
= $false )
| ( ( public @ ( enc @ ( inv @ SV4 ) @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(126,plain,
! [SV5: $i,SV16: $i] :
( ( ( public @ SV16 )
= $false )
| ( ( public @ SV5 )
= $false )
| ( ( public @ ( enc @ ( enc @ ( inv @ ( xor @ data @ km ) ) @ SV5 ) @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV22: $i,SV6: $i,SV17: $i] :
( ( ( ~ ( public @ SV17 ) )
= $true )
| ( ( ~ ( public @ ( enc @ ( xor @ SV6 @ SV17 ) @ SV22 ) ) )
= $true )
| ( ( ~ ( public @ ( enc @ ( xor @ km @ imp ) @ SV6 ) ) )
= $true )
| ( ( public @ ( enc @ ( xor @ km @ SV17 ) @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV7: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( public @ ( kp @ SV18 ) ) )
= $true )
| ( ( ~ ( public @ SV23 ) )
= $true )
| ( ( ~ ( public @ ( enc @ ( xor @ km @ ( kp @ SV18 ) ) @ SV7 ) ) )
= $true )
| ( ( public @ ( enc @ ( xor @ km @ SV18 ) @ ( xor @ SV7 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV22: $i,SV6: $i,SV17: $i] :
( ( ( public @ SV17 )
= $false )
| ( ( ~ ( public @ ( enc @ ( xor @ SV6 @ SV17 ) @ SV22 ) ) )
= $true )
| ( ( ~ ( public @ ( enc @ ( xor @ km @ imp ) @ SV6 ) ) )
= $true )
| ( ( public @ ( enc @ ( xor @ km @ SV17 ) @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(130,plain,
! [SV7: $i,SV23: $i,SV18: $i] :
( ( ( public @ ( kp @ SV18 ) )
= $false )
| ( ( ~ ( public @ SV23 ) )
= $true )
| ( ( ~ ( public @ ( enc @ ( xor @ km @ ( kp @ SV18 ) ) @ SV7 ) ) )
= $true )
| ( ( public @ ( enc @ ( xor @ km @ SV18 ) @ ( xor @ SV7 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(131,plain,
! [SV22: $i,SV17: $i,SV6: $i] :
( ( ( public @ ( enc @ ( xor @ SV6 @ SV17 ) @ SV22 ) )
= $false )
| ( ( public @ SV17 )
= $false )
| ( ( ~ ( public @ ( enc @ ( xor @ km @ imp ) @ SV6 ) ) )
= $true )
| ( ( public @ ( enc @ ( xor @ km @ SV17 ) @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(132,plain,
! [SV7: $i,SV18: $i,SV23: $i] :
( ( ( public @ SV23 )
= $false )
| ( ( public @ ( kp @ SV18 ) )
= $false )
| ( ( ~ ( public @ ( enc @ ( xor @ km @ ( kp @ SV18 ) ) @ SV7 ) ) )
= $true )
| ( ( public @ ( enc @ ( xor @ km @ SV18 ) @ ( xor @ SV7 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(133,plain,
! [SV22: $i,SV17: $i,SV6: $i] :
( ( ( public @ ( enc @ ( xor @ km @ imp ) @ SV6 ) )
= $false )
| ( ( public @ SV17 )
= $false )
| ( ( public @ ( enc @ ( xor @ SV6 @ SV17 ) @ SV22 ) )
= $false )
| ( ( public @ ( enc @ ( xor @ km @ SV17 ) @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(134,plain,
! [SV23: $i,SV7: $i,SV18: $i] :
( ( ( public @ ( enc @ ( xor @ km @ ( kp @ SV18 ) ) @ SV7 ) )
= $false )
| ( ( public @ ( kp @ SV18 ) )
= $false )
| ( ( public @ SV23 )
= $false )
| ( ( public @ ( enc @ ( xor @ km @ SV18 ) @ ( xor @ SV7 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(135,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,134,133,126,125,124,123,110,104,101,100,92,91,90,78,77,76,75,74,73,72,71]) ).
thf(136,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV234+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 16:25:59 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.15/0.91
% 4.15/0.91 No.of.Axioms: 21
% 4.15/0.91
% 4.15/0.91 Length.of.Defs: 0
% 4.15/0.91
% 4.15/0.91 Contains.Choice.Funs: false
% 4.15/0.91 ...
% 4.15/0.91
% 4.15/0.91 ********************************
% 4.15/0.91 * All subproblems solved! *
% 4.15/0.91 ********************************
% 4.15/0.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:135,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.15/0.91
% 4.15/0.91 %**** Beginning of derivation protocol ****
% 4.15/0.91 % SZS output start CNFRefutation
% See solution above
% 4.15/0.91
% 4.15/0.91 %**** End of derivation protocol ****
% 4.15/0.91 %**** no. of clauses in derivation: 136 ****
% 4.15/0.91 %**** clause counter: 135 ****
% 4.15/0.91
% 4.15/0.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:135,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------