TSTP Solution File: LAT259-2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LAT259-2 : 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 : n026.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 : Sun Jul 17 05:45:16 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 59 ( 34 unt; 13 typ; 0 def)
% Number of atoms : 201 ( 75 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 520 ( 43 ~; 49 |; 0 &; 428 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 9 con; 0-4 aty)
% Number of variables : 70 ( 0 ^ 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_Oantisym,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(tp_c_Tarski_OPartialOrder,type,
c_Tarski_OPartialOrder: $i ).
thf(tp_c_Tarski_Opotype_Oorder,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
thf(tp_tc_Tarski_Opotype_Opotype__ext__type,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_v_a,type,
v_a: $i ).
thf(tp_v_b,type,
v_b: $i ).
thf(tp_v_cl,type,
v_cl: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(1,axiom,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(2,axiom,
c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
thf(3,axiom,
! [V_P: $i,T_a: $i] :
( ~ ( c_in @ V_P @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ V_P @ T_a @ tc_Product__Type_Ounit ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_1) ).
thf(4,axiom,
! [V_r: $i,T_a: $i,V_V: $i,V_U: $i] :
( ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ V_V @ V_U @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_U @ V_V @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_U = V_V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oantisym__def_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,
v_a != v_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(8,negated_conjecture,
c_in @ ( c_Pair @ v_b @ v_a @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(9,negated_conjecture,
c_in @ ( c_Pair @ v_a @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(11,plain,
( ( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [V_P: $i,T_a: $i] :
( ~ ( c_in @ V_P @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ V_P @ T_a @ tc_Product__Type_Ounit ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [V_r: $i,T_a: $i,V_V: $i,V_U: $i] :
( ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ V_V @ V_U @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_U @ V_V @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_U = V_V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ( v_a != v_b ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(16,plain,
( ( c_in @ ( c_Pair @ v_b @ v_a @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(17,plain,
( ( c_in @ ( c_Pair @ v_a @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [V_r: $i,T_a: $i] :
( ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ! [V_V: $i,V_U: $i] :
( ~ ( c_in @ ( c_Pair @ V_V @ V_U @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_U @ V_V @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_U = V_V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(20,plain,
( ( ( v_a != v_b ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(21,plain,
( ( c_in @ ( c_Pair @ v_a @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(22,plain,
( ( c_in @ ( c_Pair @ v_b @ v_a @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(23,plain,
( ( ( v_a != v_b ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [V_r: $i,T_a: $i] :
( ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ! [V_V: $i,V_U: $i] :
( ~ ( c_in @ ( c_Pair @ V_V @ V_U @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_U @ V_V @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_U = V_V ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(25,plain,
( ( ! [V_P: $i,T_a: $i] :
( ~ ( c_in @ V_P @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ V_P @ T_a @ tc_Product__Type_Ounit ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(26,plain,
( ( c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(27,plain,
( ( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(28,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(29,plain,
( ( v_a = v_b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV1: $i] :
( ( ! [SY6: $i] :
( ~ ( c_Relation_Oantisym @ SV1 @ SY6 )
| ! [SY7: $i,SY8: $i] :
( ~ ( c_in @ ( c_Pair @ SY7 @ SY8 @ SY6 @ SY6 ) @ SV1 @ ( tc_prod @ SY6 @ SY6 ) )
| ~ ( c_in @ ( c_Pair @ SY8 @ SY7 @ SY6 @ SY6 ) @ SV1 @ ( tc_prod @ SY6 @ SY6 ) )
| ( SY8 = SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV2: $i] :
( ( ! [SY9: $i] :
( ~ ( c_in @ SV2 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SY9 @ tc_Product__Type_Ounit ) )
| ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ SV2 @ SY9 @ tc_Product__Type_Ounit ) @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( c_Relation_Oantisym @ SV1 @ SV3 )
| ! [SY10: $i,SY11: $i] :
( ~ ( c_in @ ( c_Pair @ SY10 @ SY11 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ~ ( c_in @ ( c_Pair @ SY11 @ SY10 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ( SY11 = SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV4 @ tc_Product__Type_Ounit ) )
| ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ SV2 @ SV4 @ tc_Product__Type_Ounit ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV1 @ SV3 ) )
= $true )
| ( ( ! [SY10: $i,SY11: $i] :
( ~ ( c_in @ ( c_Pair @ SY10 @ SY11 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ~ ( c_in @ ( c_Pair @ SY11 @ SY10 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ( SY11 = SY10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV4 @ tc_Product__Type_Ounit ) ) )
= $true )
| ( ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ SV2 @ SV4 @ tc_Product__Type_Ounit ) @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: $i,SV1: $i] :
( ( ( c_Relation_Oantisym @ SV1 @ SV3 )
= $false )
| ( ( ! [SY10: $i,SY11: $i] :
( ~ ( c_in @ ( c_Pair @ SY10 @ SY11 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ~ ( c_in @ ( c_Pair @ SY11 @ SY10 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ( SY11 = SY10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV4: $i,SV2: $i] :
( ( ( c_in @ SV2 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV4 @ tc_Product__Type_Ounit ) )
= $false )
| ( ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ SV2 @ SV4 @ tc_Product__Type_Ounit ) @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV1: $i,SV3: $i,SV5: $i] :
( ( ( ! [SY12: $i] :
( ~ ( c_in @ ( c_Pair @ SV5 @ SY12 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ~ ( c_in @ ( c_Pair @ SY12 @ SV5 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ( SY12 = SV5 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV1: $i,SV3: $i,SV6: $i,SV5: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV5 @ SV6 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ~ ( c_in @ ( c_Pair @ SV6 @ SV5 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ( SV6 = SV5 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(41,plain,
! [SV1: $i,SV3: $i,SV6: $i,SV5: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV5 @ SV6 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV6 @ SV5 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ( SV6 = SV5 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(42,plain,
! [SV1: $i,SV3: $i,SV6: $i,SV5: $i] :
( ( ( c_in @ ( c_Pair @ SV5 @ SV6 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV6 @ SV5 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
| ( SV6 = SV5 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(43,plain,
! [SV1: $i,SV3: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV6 @ SV5 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) ) )
= $true )
| ( ( SV6 = SV5 )
= $true )
| ( ( c_in @ ( c_Pair @ SV5 @ SV6 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV1: $i,SV3: $i,SV5: $i,SV6: $i] :
( ( ( c_in @ ( c_Pair @ SV6 @ SV5 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
= $false )
| ( ( SV6 = SV5 )
= $true )
| ( ( c_in @ ( c_Pair @ SV5 @ SV6 @ SV3 @ SV3 ) @ SV1 @ ( tc_prod @ SV3 @ SV3 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(45,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,44,38,32,29,27,26,22]) ).
thf(46,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT259-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 30 12:26:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 7
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (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/sandbox2/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:45,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.40
% 0.19/0.40 %**** Beginning of derivation protocol ****
% 0.19/0.40 % SZS output start CNFRefutation
% See solution above
% 0.19/0.40
% 0.19/0.40 %**** End of derivation protocol ****
% 0.19/0.40 %**** no. of clauses in derivation: 46 ****
% 0.19/0.40 %**** clause counter: 45 ****
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/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:45,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------