%------------------------------------------------------------------------------
% 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 : n019.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 : Unsatisfiable 0.07s 0.20s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 66 ( 19 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 86 ( 13 ~; 7 |; 0 &; 66 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_a_holds,type,
a_holds: $i > $o ).
thf(tp_an_a_nonce,type,
an_a_nonce: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_b_holds,type,
b_holds: $i > $o ).
thf(tp_generate_key,type,
generate_key: $i > $i ).
thf(tp_key,type,
key: $i > $i > $i ).
thf(1,axiom,
a_holds @ ( key @ ( generate_key @ an_a_nonce ) @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_13) ).
thf(2,axiom,
b_holds @ ( key @ ( generate_key @ an_a_nonce ) @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_11) ).
thf(3,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(4,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,negated_conjecture,
! [A: $i] :
( ~ ( a_holds @ ( key @ A @ b ) )
| ~ ( b_holds @ ( key @ A @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
thf(6,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(7,plain,
( ( a_holds @ ( key @ ( generate_key @ an_a_nonce ) @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( b_holds @ ( key @ ( generate_key @ an_a_nonce ) @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [A: $i] :
( ~ ( a_holds @ ( key @ A @ b ) )
| ~ ( b_holds @ ( key @ A @ a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [A: $i] :
( ~ ( a_holds @ ( key @ A @ b ) )
| ~ ( b_holds @ ( key @ A @ a ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( b_holds @ ( key @ ( generate_key @ an_a_nonce ) @ a ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( a_holds @ ( key @ ( generate_key @ an_a_nonce ) @ b ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
! [SV1: $i] :
( ( ~ ( a_holds @ ( key @ SV1 @ b ) )
| ~ ( b_holds @ ( key @ SV1 @ a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV1: $i] :
( ( ( ~ ( a_holds @ ( key @ SV1 @ b ) ) )
= $true )
| ( ( ~ ( b_holds @ ( key @ SV1 @ a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: $i] :
( ( ( a_holds @ ( key @ SV1 @ b ) )
= $false )
| ( ( ~ ( b_holds @ ( key @ SV1 @ a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: $i] :
( ( ( b_holds @ ( key @ SV1 @ a ) )
= $false )
| ( ( a_holds @ ( key @ SV1 @ b ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[12,19,16,13]) ).
thf(21,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV011-1 : TPTP v9.3.1. Released v2.4.0.
% 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
% 0.07/0.17 % Computer : n019.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 16:16:55 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20
% 0.07/0.20 No.of.Axioms: 3
% 0.07/0.20
% 0.07/0.20 Length.of.Defs: 0
% 0.07/0.20
% 0.07/0.20 Contains.Choice.Funs: false
% 0.07/0.20
% 0.07/0.20 ********************************
% 0.07/0.20 * All subproblems solved! *
% 0.07/0.20 ********************************
% 0.07/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:20,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.20
% 0.07/0.20 %**** Beginning of derivation protocol ****
% 0.07/0.20 % SZS output start CNFRefutation
% See solution above
% 0.07/0.20
% 0.07/0.20 %**** End of derivation protocol ****
% 0.07/0.20 %**** no. of clauses in derivation: 21 ****
% 0.07/0.20 %**** clause counter: 20 ****
% 0.07/0.20
% 0.07/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:20,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------