%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV011+1 : TPTP v9.3.1. Released v2.4.0.
% 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 : n014.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 10:54:27 AM UTC 2026
% Result : Theorem 0.08s 0.22s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 134 ( 37 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 211 ( 29 ~; 9 |; 5 &; 168 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 8 con; 0-4 aty)
% Number of variables : 14 ( 0 ^; 9 !; 5 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_a_holds,type,
a_holds: $i > $o ).
thf(tp_a_stored,type,
a_stored: $i > $o ).
thf(tp_an_a_nonce,type,
an_a_nonce: $i ).
thf(tp_at,type,
at: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_b_holds,type,
b_holds: $i > $o ).
thf(tp_b_stored,type,
b_stored: $i > $o ).
thf(tp_bt,type,
bt: $i ).
thf(tp_encrypt,type,
encrypt: $i > $i > $i ).
thf(tp_fresh_to_b,type,
fresh_to_b: $i > $o ).
thf(tp_generate_b_nonce,type,
generate_b_nonce: $i > $i ).
thf(tp_generate_expiration_time,type,
generate_expiration_time: $i > $i ).
thf(tp_generate_key,type,
generate_key: $i > $i ).
thf(tp_key,type,
key: $i > $i > $i ).
thf(tp_message,type,
message: $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_party_of_protocol,type,
party_of_protocol: $i > $o ).
thf(tp_quadruple,type,
quadruple: $i > $i > $i > $i > $i ).
thf(tp_sent,type,
sent: $i > $i > $i > $i ).
thf(tp_t,type,
t: $i ).
thf(tp_t_holds,type,
t_holds: $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(1,axiom,
b_stored @ ( pair @ a @ an_a_nonce ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(4,axiom,
a_holds @ ( key @ ( generate_key @ an_a_nonce ) @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(6,axiom,
b_holds @ ( key @ ( generate_key @ an_a_nonce ) @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(8,axiom,
t_holds @ ( key @ bt @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_holds_key_bt_for_b) ).
thf(9,axiom,
t_holds @ ( key @ at @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_holds_key_at_for_a) ).
thf(11,axiom,
party_of_protocol @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_party_of_protocol) ).
thf(12,axiom,
b_holds @ ( key @ bt @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_hold_key_bt_for_t) ).
thf(13,axiom,
a_stored @ ( pair @ b @ an_a_nonce ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_stored_message_i) ).
thf(15,axiom,
party_of_protocol @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_party_of_protocol) ).
thf(16,axiom,
a_holds @ ( key @ at @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_holds_key_at_for_t) ).
thf(17,conjecture,
? [U: $i] :
( ( a_holds @ ( key @ U @ b ) )
& ( b_holds @ ( key @ U @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(18,negated_conjecture,
( ( ? [U: $i] :
( ( a_holds @ ( key @ U @ b ) )
& ( b_holds @ ( key @ U @ a ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,plain,
( ( ? [U: $i] :
( ( a_holds @ ( key @ U @ b ) )
& ( b_holds @ ( key @ U @ a ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[18]) ).
thf(20,plain,
( ( b_stored @ ( pair @ a @ an_a_nonce ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(21,plain,
( ( a_holds @ ( key @ ( generate_key @ an_a_nonce ) @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
( ( b_holds @ ( key @ ( generate_key @ an_a_nonce ) @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( t_holds @ ( key @ bt @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( t_holds @ ( key @ at @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( party_of_protocol @ b )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( b_holds @ ( key @ bt @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(27,plain,
( ( a_stored @ ( pair @ b @ an_a_nonce ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(28,plain,
( ( party_of_protocol @ a )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(29,plain,
( ( a_holds @ ( key @ at @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(30,plain,
( ( ~ ? [U: $i] :
( ( a_holds @ ( key @ U @ b ) )
& ( b_holds @ ( key @ U @ a ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(31,plain,
( ( a_holds @ ( key @ at @ t ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(32,plain,
( ( party_of_protocol @ a )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(33,plain,
( ( a_stored @ ( pair @ b @ an_a_nonce ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(34,plain,
( ( b_holds @ ( key @ bt @ t ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(35,plain,
( ( party_of_protocol @ b )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(36,plain,
( ( t_holds @ ( key @ at @ a ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(37,plain,
( ( t_holds @ ( key @ bt @ b ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(38,plain,
( ( b_holds @ ( key @ ( generate_key @ an_a_nonce ) @ a ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(39,plain,
( ( a_holds @ ( key @ ( generate_key @ an_a_nonce ) @ b ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(40,plain,
( ( b_stored @ ( pair @ a @ an_a_nonce ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(41,plain,
( ( ~ ? [U: $i] :
( ( a_holds @ ( key @ U @ b ) )
& ( b_holds @ ( key @ U @ a ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(42,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( a_holds @ ( key @ SX0 @ b ) )
| ~ ( b_holds @ ( key @ SX0 @ a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(43,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( a_holds @ ( key @ SX0 @ b ) )
| ~ ( b_holds @ ( key @ SX0 @ a ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( a_holds @ ( key @ SX0 @ b ) )
| ~ ( b_holds @ ( key @ SX0 @ a ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(45,plain,
! [SV1: $i] :
( ( ~ ~ ( ~ ( a_holds @ ( key @ SV1 @ b ) )
| ~ ( b_holds @ ( key @ SV1 @ a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(46,plain,
! [SV1: $i] :
( ( ~ ( ~ ( a_holds @ ( key @ SV1 @ b ) )
| ~ ( b_holds @ ( key @ SV1 @ a ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(47,plain,
! [SV1: $i] :
( ( ~ ( a_holds @ ( key @ SV1 @ b ) )
| ~ ( b_holds @ ( key @ SV1 @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(48,plain,
! [SV1: $i] :
( ( ( ~ ( a_holds @ ( key @ SV1 @ b ) ) )
= $true )
| ( ( ~ ( b_holds @ ( key @ SV1 @ a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV1: $i] :
( ( ( a_holds @ ( key @ SV1 @ b ) )
= $false )
| ( ( ~ ( b_holds @ ( key @ SV1 @ a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV1: $i] :
( ( ( b_holds @ ( key @ SV1 @ a ) )
= $false )
| ( ( a_holds @ ( key @ SV1 @ b ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,50,40,39,38,37,36,35,34,33,32]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV011+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % 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 : n014.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 16:16:35 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
% 0.08/0.22
% 0.08/0.22 No.of.Axioms: 10
% 0.08/0.22
% 0.08/0.22 Length.of.Defs: 0
% 0.08/0.22
% 0.08/0.22 Contains.Choice.Funs: false
% 0.08/0.22
% 0.08/0.22 ********************************
% 0.08/0.22 * All subproblems solved! *
% 0.08/0.22 ********************************
% 0.08/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:51,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.22
% 0.08/0.22 %**** Beginning of derivation protocol ****
% 0.08/0.22 % SZS output start CNFRefutation
% See solution above
% 0.08/0.22
% 0.08/0.22 %**** End of derivation protocol ****
% 0.08/0.22 %**** no. of clauses in derivation: 46 ****
% 0.08/0.22 %**** clause counter: 51 ****
% 0.08/0.22
% 0.08/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:51,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------