%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV267-2 : 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 : n001.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 10:56:52 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.19s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 119 ( 32 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 250 ( 24 ~; 24 |; 0 &; 202 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Message_Oparts,type,
c_Message_Oparts: $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_tc_Message_Omsg,type,
tc_Message_Omsg: $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_G,type,
v_G: $i ).
thf(tp_v_H,type,
v_H: $i ).
thf(1,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
thf(2,axiom,
! [V_H: $i] : ( c_lessequals @ V_H @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__increasing_0) ).
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,
~ ( c_lessequals @ v_G @ ( c_Message_Oparts @ v_H ) @ ( tc_set @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(6,negated_conjecture,
c_lessequals @ ( c_Message_Oparts @ v_G ) @ ( c_Message_Oparts @ v_H ) @ ( tc_set @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(8,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [V_H: $i] : ( c_lessequals @ V_H @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ~ ( c_lessequals @ v_G @ ( c_Message_Oparts @ v_H ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(11,plain,
( ( c_lessequals @ ( c_Message_Oparts @ v_G ) @ ( c_Message_Oparts @ v_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( c_lessequals @ ( c_Message_Oparts @ v_G ) @ ( c_Message_Oparts @ v_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ( c_lessequals @ v_G @ ( c_Message_Oparts @ v_H ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [V_H: $i] : ( c_lessequals @ V_H @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(18,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
( ( c_lessequals @ v_G @ ( c_Message_Oparts @ v_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV1: $i] :
( ( c_lessequals @ SV1 @ ( c_Message_Oparts @ SV1 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV2: $i] :
( ( ! [SY5: $i,SY6: $i] :
( ~ ( c_lessequals @ SV2 @ SY5 @ ( tc_set @ SY6 ) )
| ! [SY7: $i] :
( ~ ( c_lessequals @ SY7 @ SV2 @ ( tc_set @ SY6 ) )
| ( c_lessequals @ SY7 @ SY5 @ ( tc_set @ SY6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: $i,SV2: $i] :
( ( ! [SY8: $i] :
( ~ ( c_lessequals @ SV2 @ SV3 @ ( tc_set @ SY8 ) )
| ! [SY9: $i] :
( ~ ( c_lessequals @ SY9 @ SV2 @ ( tc_set @ SY8 ) )
| ( c_lessequals @ SY9 @ SV3 @ ( tc_set @ SY8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ~ ( c_lessequals @ SV2 @ SV3 @ ( tc_set @ SV4 ) )
| ! [SY10: $i] :
( ~ ( c_lessequals @ SY10 @ SV2 @ ( tc_set @ SV4 ) )
| ( c_lessequals @ SY10 @ SV3 @ ( tc_set @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(25,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( c_lessequals @ SV2 @ SV3 @ ( tc_set @ SV4 ) ) )
= $true )
| ( ( ! [SY10: $i] :
( ~ ( c_lessequals @ SY10 @ SV2 @ ( tc_set @ SV4 ) )
| ( c_lessequals @ SY10 @ SV3 @ ( tc_set @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( c_lessequals @ SV2 @ SV3 @ ( tc_set @ SV4 ) )
= $false )
| ( ( ! [SY10: $i] :
( ~ ( c_lessequals @ SY10 @ SV2 @ ( tc_set @ SV4 ) )
| ( c_lessequals @ SY10 @ SV3 @ ( tc_set @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV3: $i,SV4: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( c_lessequals @ SV5 @ SV2 @ ( tc_set @ SV4 ) )
| ( c_lessequals @ SV5 @ SV3 @ ( tc_set @ SV4 ) ) )
= $true )
| ( ( c_lessequals @ SV2 @ SV3 @ ( tc_set @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV3: $i,SV4: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( c_lessequals @ SV5 @ SV2 @ ( tc_set @ SV4 ) ) )
= $true )
| ( ( c_lessequals @ SV5 @ SV3 @ ( tc_set @ SV4 ) )
= $true )
| ( ( c_lessequals @ SV2 @ SV3 @ ( tc_set @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(29,plain,
! [SV3: $i,SV4: $i,SV2: $i,SV5: $i] :
( ( ( c_lessequals @ SV5 @ SV2 @ ( tc_set @ SV4 ) )
= $false )
| ( ( c_lessequals @ SV5 @ SV3 @ ( tc_set @ SV4 ) )
= $true )
| ( ( c_lessequals @ SV2 @ SV3 @ ( tc_set @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(30,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,29,22,20,19]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV267-2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.15 % Computer : n001.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Oct 6 16:28:09 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.19
% 0.09/0.19 No.of.Axioms: 4
% 0.09/0.19
% 0.09/0.19 Length.of.Defs: 0
% 0.09/0.19
% 0.09/0.19 Contains.Choice.Funs: false
% 0.09/0.19
% 0.09/0.19 ********************************
% 0.09/0.19 * All subproblems solved! *
% 0.09/0.19 ********************************
% 0.09/0.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:30,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.19
% 0.09/0.19 %**** Beginning of derivation protocol ****
% 0.09/0.19 % SZS output start CNFRefutation
% See solution above
% 0.09/0.19
% 0.09/0.19 %**** End of derivation protocol ****
% 0.09/0.19 %**** no. of clauses in derivation: 31 ****
% 0.09/0.19 %**** clause counter: 30 ****
% 0.09/0.19
% 0.09/0.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:30,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------