%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV253-2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 10:56:39 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.18s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 48 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 54 ( 13 ~; 11 |; 0 &; 30 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Message_OinvKey,type,
c_Message_OinvKey: $i > $i ).
thf(tp_v_K,type,
v_K: $i ).
thf(tp_v_K_H,type,
v_K_H: $i ).
thf(1,axiom,
! [V_y: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ V_y ) )
= V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
thf(2,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(3,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,negated_conjecture,
( ( ( c_Message_OinvKey @ v_K )
= ( c_Message_OinvKey @ v_K_H ) )
| ( v_K = v_K_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(5,negated_conjecture,
( ( v_K != v_K_H )
| ( ( c_Message_OinvKey @ v_K )
!= ( c_Message_OinvKey @ v_K_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(6,plain,
$false = $false,
inference(unfold_def,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [V_y: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ V_y ) )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ( ( c_Message_OinvKey @ v_K )
= ( c_Message_OinvKey @ v_K_H ) )
| ( v_K = v_K_H ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(9,plain,
( ( ( v_K != v_K_H )
| ( ( c_Message_OinvKey @ v_K )
!= ( c_Message_OinvKey @ v_K_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ( v_K != v_K_H )
| ( ( c_Message_OinvKey @ v_K )
!= ( c_Message_OinvKey @ v_K_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(12,plain,
( ( ( v_K != v_K_H )
| ( ( c_Message_OinvKey @ v_K )
!= ( c_Message_OinvKey @ v_K_H ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(13,plain,
( ( ( ( c_Message_OinvKey @ v_K )
= ( c_Message_OinvKey @ v_K_H ) )
| ( v_K = v_K_H ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ! [V_y: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ V_y ) )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(15,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ( v_K != v_K_H )
= $true )
| ( ( ( c_Message_OinvKey @ v_K )
!= ( c_Message_OinvKey @ v_K_H ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ( ( c_Message_OinvKey @ v_K )
= ( c_Message_OinvKey @ v_K_H ) )
= $true )
| ( ( v_K = v_K_H )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV1: $i] :
( ( ( c_Message_OinvKey @ ( c_Message_OinvKey @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( ( v_K = v_K_H )
= $false )
| ( ( ( c_Message_OinvKey @ v_K )
!= ( c_Message_OinvKey @ v_K_H ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ( ( c_Message_OinvKey @ v_K )
= ( c_Message_OinvKey @ v_K_H ) )
= $false )
| ( ( v_K = v_K_H )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(22,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,21,19,18]) ).
thf(23,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV253-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.15 % Computer : n004.cluster.edu
% 0.12/0.15 % Model : x86_64 x86_64
% 0.12/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.15 % Memory : 8046.5625MB
% 0.12/0.15 % OS : Linux 6.8.0-71-generic
% 0.12/0.15 % CPULimit : 300
% 0.12/0.15 % WCLimit : 300
% 0.12/0.15 % DateTime : Tue Oct 6 16:21:39 UTC 2026
% 0.12/0.16 % CPUTime :
% 0.12/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.18
% 0.12/0.18 No.of.Axioms: 3
% 0.12/0.18
% 0.12/0.18 Length.of.Defs: 0
% 0.12/0.18
% 0.12/0.18 Contains.Choice.Funs: false
% 0.12/0.18
% 0.12/0.18 ********************************
% 0.12/0.18 * All subproblems solved! *
% 0.12/0.18 ********************************
% 0.12/0.18 % SZS status Unsatisfiable for /export/starexec/sandbox/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:22,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.18
% 0.12/0.18 %**** Beginning of derivation protocol ****
% 0.12/0.18 % SZS output start CNFRefutation
% See solution above
% 0.12/0.18
% 0.12/0.18 %**** End of derivation protocol ****
% 0.12/0.18 %**** no. of clauses in derivation: 23 ****
% 0.12/0.18 %**** clause counter: 22 ****
% 0.12/0.18
% 0.12/0.18 % SZS status Unsatisfiable for /export/starexec/sandbox/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:22,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------