TSTP Solution File: SWV242-2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV242-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:11:19 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 60 ( 38 unt; 9 typ; 0 def)
% Number of atoms : 196 ( 54 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 497 ( 36 ~; 37 |; 0 &; 424 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 98 ( 0 ^ 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Message_Oanalz,type,
c_Message_Oanalz: $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_union,type,
c_union: $i > $i > $i > $i ).
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_G_H,type,
v_G_H: $i ).
thf(tp_v_H,type,
v_H: $i ).
thf(tp_v_H_H,type,
v_H_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/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
thf(2,axiom,
! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__upper2_0) ).
thf(3,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__upper1_0) ).
thf(4,axiom,
! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__mono_0) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
( ~ ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(8,negated_conjecture,
c_lessequals @ v_H @ ( c_Message_Oanalz @ v_H_H ) @ ( tc_set @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(9,negated_conjecture,
c_lessequals @ v_G @ ( c_Message_Oanalz @ v_G_H ) @ ( tc_set @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(11,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(12,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ~ ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(16,plain,
( ( c_lessequals @ v_H @ ( c_Message_Oanalz @ v_H_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(17,plain,
( ( c_lessequals @ v_G @ ( c_Message_Oanalz @ v_G_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,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)],[11]) ).
thf(20,plain,
( ( c_lessequals @ v_G @ ( c_Message_Oanalz @ v_G_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(21,plain,
( ( c_lessequals @ v_H @ ( c_Message_Oanalz @ v_H_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(22,plain,
( ( ~ ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(23,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(24,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(25,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(26,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)],[19]) ).
thf(27,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(28,plain,
( ( ( ~ ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true )
| ( ( ~ ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV1: $i] :
( ( ! [SY12: $i] :
( ~ ( c_lessequals @ SV1 @ SY12 @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ SV1 ) @ ( c_Message_Oanalz @ SY12 ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV2: $i] :
( ( ! [SY13: $i,SY14: $i] : ( c_lessequals @ SV2 @ ( c_union @ SV2 @ SY13 @ SY14 ) @ ( tc_set @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV3: $i] :
( ( ! [SY15: $i,SY16: $i] : ( c_lessequals @ SV3 @ ( c_union @ SY15 @ SV3 @ SY16 ) @ ( tc_set @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV4: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ~ ( c_lessequals @ SV4 @ SY17 @ ( tc_set @ SY18 ) )
| ! [SY19: $i] :
( ~ ( c_lessequals @ SY19 @ SV4 @ ( tc_set @ SY18 ) )
| ( c_lessequals @ SY19 @ SY17 @ ( tc_set @ SY18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(34,plain,
( ( ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
= $false )
| ( ( ~ ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV5: $i,SV1: $i] :
( ( ~ ( c_lessequals @ SV1 @ SV5 @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ SV1 ) @ ( c_Message_Oanalz @ SV5 ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY20: $i] : ( c_lessequals @ SV2 @ ( c_union @ SV2 @ SV6 @ SY20 ) @ ( tc_set @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY21: $i] : ( c_lessequals @ SV3 @ ( c_union @ SV7 @ SV3 @ SY21 ) @ ( tc_set @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV8: $i,SV4: $i] :
( ( ! [SY22: $i] :
( ~ ( c_lessequals @ SV4 @ SV8 @ ( tc_set @ SY22 ) )
| ! [SY23: $i] :
( ~ ( c_lessequals @ SY23 @ SV4 @ ( tc_set @ SY22 ) )
| ( c_lessequals @ SY23 @ SV8 @ ( tc_set @ SY22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
( ( ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
= $false )
| ( ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV5: $i,SV1: $i] :
( ( ( ~ ( c_lessequals @ SV1 @ SV5 @ ( tc_set @ tc_Message_Omsg ) ) )
= $true )
| ( ( c_lessequals @ ( c_Message_Oanalz @ SV1 ) @ ( c_Message_Oanalz @ SV5 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV9: $i,SV6: $i,SV2: $i] :
( ( c_lessequals @ SV2 @ ( c_union @ SV2 @ SV6 @ SV9 ) @ ( tc_set @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( c_lessequals @ SV3 @ ( c_union @ SV7 @ SV3 @ SV10 ) @ ( tc_set @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ~ ( c_lessequals @ SV4 @ SV8 @ ( tc_set @ SV11 ) )
| ! [SY24: $i] :
( ~ ( c_lessequals @ SY24 @ SV4 @ ( tc_set @ SV11 ) )
| ( c_lessequals @ SY24 @ SV8 @ ( tc_set @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV5: $i,SV1: $i] :
( ( ( c_lessequals @ SV1 @ SV5 @ ( tc_set @ tc_Message_Omsg ) )
= $false )
| ( ( c_lessequals @ ( c_Message_Oanalz @ SV1 ) @ ( c_Message_Oanalz @ SV5 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( c_lessequals @ SV4 @ SV8 @ ( tc_set @ SV11 ) ) )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( c_lessequals @ SY24 @ SV4 @ ( tc_set @ SV11 ) )
| ( c_lessequals @ SY24 @ SV8 @ ( tc_set @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( c_lessequals @ SV4 @ SV8 @ ( tc_set @ SV11 ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( c_lessequals @ SY24 @ SV4 @ ( tc_set @ SV11 ) )
| ( c_lessequals @ SY24 @ SV8 @ ( tc_set @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(47,plain,
! [SV8: $i,SV11: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( c_lessequals @ SV12 @ SV4 @ ( tc_set @ SV11 ) )
| ( c_lessequals @ SV12 @ SV8 @ ( tc_set @ SV11 ) ) )
= $true )
| ( ( c_lessequals @ SV4 @ SV8 @ ( tc_set @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV8: $i,SV11: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( c_lessequals @ SV12 @ SV4 @ ( tc_set @ SV11 ) ) )
= $true )
| ( ( c_lessequals @ SV12 @ SV8 @ ( tc_set @ SV11 ) )
= $true )
| ( ( c_lessequals @ SV4 @ SV8 @ ( tc_set @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV8: $i,SV11: $i,SV4: $i,SV12: $i] :
( ( ( c_lessequals @ SV12 @ SV4 @ ( tc_set @ SV11 ) )
= $false )
| ( ( c_lessequals @ SV12 @ SV8 @ ( tc_set @ SV11 ) )
= $true )
| ( ( c_lessequals @ SV4 @ SV8 @ ( tc_set @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(50,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,49,44,42,41,39,33,21]) ).
thf(51,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV242-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 22:00:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 7
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:7,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:9,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.39
% 0.19/0.39 ********************************
% 0.19/0.39 * All subproblems solved! *
% 0.19/0.39 ********************************
% 0.19/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:50,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.39
% 0.19/0.39 %**** Beginning of derivation protocol ****
% 0.19/0.39 % SZS output start CNFRefutation
% See solution above
% 0.19/0.39
% 0.19/0.39 %**** End of derivation protocol ****
% 0.19/0.39 %**** no. of clauses in derivation: 51 ****
% 0.19/0.39 %**** clause counter: 50 ****
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:50,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------