TSTP Solution File: SET825-2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET825-2 : 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 : n027.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 : Tue Jul 19 03:05:19 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of formulae : 56 ( 31 unt; 12 typ; 0 def)
% Number of atoms : 185 ( 60 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 655 ( 32 ~; 39 |; 0 &; 584 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 52 ( 0 ^ 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_0,type,
c_0: $i ).
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_OId,type,
c_Relation_OId: $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_v_Q,type,
v_Q: $i > $o ).
thf(tp_v_m,type,
v_m: $i ).
thf(tp_v_n,type,
v_n: $i ).
thf(tp_v_x,type,
v_x: $i > $i ).
thf(tp_v_xa,type,
v_xa: $i > $i ).
thf(1,axiom,
! [V_a: $i,V_b: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(2,axiom,
! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_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,
! [V_U: $i] :
( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ ( c_Suc @ ( v_x @ V_U ) ) @ ( c_Suc @ ( v_xa @ V_U ) ) @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(6,negated_conjecture,
! [V_U: $i] :
( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_in @ ( c_Pair @ ( v_x @ V_U ) @ ( v_xa @ V_U ) @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(7,negated_conjecture,
~ ( v_Q @ v_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,negated_conjecture,
v_Q @ v_n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(10,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ ( c_Suc @ ( v_x @ V_U ) ) @ ( c_Suc @ ( v_xa @ V_U ) ) @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_in @ ( c_Pair @ ( v_x @ V_U ) @ ( v_xa @ V_U ) @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(14,plain,
( ( ~ ( v_Q @ v_m ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(15,plain,
( ( v_Q @ v_n )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [V_a: $i,V_b: $i] :
( ! [T_a: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(18,plain,
( ( v_Q @ v_n )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( v_Q @ v_m ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_in @ ( c_Pair @ ( v_x @ V_U ) @ ( v_xa @ V_U ) @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ ( c_Suc @ ( v_x @ V_U ) ) @ ( c_Suc @ ( v_xa @ V_U ) ) @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ V_U @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [V_a: $i,V_b: $i] :
( ! [T_a: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( v_Q @ v_m )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_in @ ( c_Pair @ ( v_x @ SV1 ) @ ( v_xa @ SV1 ) @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ ( c_Suc @ ( v_x @ SV2 ) ) @ ( c_Suc @ ( v_xa @ SV2 ) ) @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV3: $i] :
( ( ! [SY7: $i] : ( c_in @ ( c_Pair @ SV3 @ SV3 @ SY7 @ SY7 ) @ c_Relation_OId @ ( tc_prod @ SY7 @ SY7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV4: $i] :
( ( ! [SY8: $i] :
( ! [SY9: $i] :
~ ( c_in @ ( c_Pair @ SV4 @ SY8 @ SY9 @ SY9 ) @ c_Relation_OId @ ( tc_prod @ SY9 @ SY9 ) )
| ( SV4 = SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ ( v_x @ SV1 ) @ ( v_xa @ SV1 ) @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( c_Suc @ ( v_x @ SV2 ) ) @ ( c_Suc @ ( v_xa @ SV2 ) ) @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV5: $i,SV3: $i] :
( ( c_in @ ( c_Pair @ SV3 @ SV3 @ SV5 @ SV5 ) @ c_Relation_OId @ ( tc_prod @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV6: $i,SV4: $i] :
( ( ! [SY10: $i] :
~ ( c_in @ ( c_Pair @ SV4 @ SV6 @ SY10 @ SY10 ) @ c_Relation_OId @ ( tc_prod @ SY10 @ SY10 ) )
| ( SV4 = SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ ( v_x @ SV1 ) @ ( v_xa @ SV1 ) @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( c_Suc @ ( v_x @ SV2 ) ) @ ( c_Suc @ ( v_xa @ SV2 ) ) @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV6: $i,SV4: $i] :
( ( ( ! [SY10: $i] :
~ ( c_in @ ( c_Pair @ SV4 @ SV6 @ SY10 @ SY10 ) @ c_Relation_OId @ ( tc_prod @ SY10 @ SY10 ) ) )
= $true )
| ( ( SV4 = SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( v_x @ SV1 ) @ ( v_xa @ SV1 ) @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true )
| ( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ SV1 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Suc @ ( v_x @ SV2 ) ) @ ( c_Suc @ ( v_xa @ SV2 ) ) @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV7: $i,SV6: $i,SV4: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV4 @ SV6 @ SV7 @ SV7 ) @ c_Relation_OId @ ( tc_prod @ SV7 @ SV7 ) ) )
= $true )
| ( ( SV4 = SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Suc @ ( v_x @ SV2 ) ) @ ( c_Suc @ ( v_xa @ SV2 ) ) @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $false )
| ( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ SV2 @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV7: $i,SV6: $i,SV4: $i] :
( ( ( c_in @ ( c_Pair @ SV4 @ SV6 @ SV7 @ SV7 ) @ c_Relation_OId @ ( tc_prod @ SV7 @ SV7 ) )
= $false )
| ( ( SV4 = SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,42,41,38,33,30,25]) ).
thf(44,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET825-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n027.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 : Sun Jul 10 06:15:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 6
% 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:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.12/0.39
% 0.12/0.39 ********************************
% 0.12/0.39 * All subproblems solved! *
% 0.12/0.39 ********************************
% 0.12/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:43,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.39
% 0.12/0.39 %**** Beginning of derivation protocol ****
% 0.12/0.39 % SZS output start CNFRefutation
% See solution above
% 0.12/0.40
% 0.12/0.40 %**** End of derivation protocol ****
% 0.12/0.40 %**** no. of clauses in derivation: 44 ****
% 0.12/0.40 %**** clause counter: 43 ****
% 0.12/0.40
% 0.12/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:43,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------