TSTP Solution File: COM004-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : COM004-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n024.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 : Fri Jul 15 01:28:33 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 68 ( 44 unt; 13 typ; 0 def)
% Number of atoms : 267 ( 76 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 553 ( 64 ~; 72 |; 0 &; 417 @)
% ( 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 : 16 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 125 ( 0 ^ 125 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_atom,type,
atom: $i ).
thf(tp_contradictory,type,
contradictory: $i > $i > $o ).
thf(tp_empty,type,
empty: $i ).
thf(tp_failure_node,type,
failure_node: $i > $i > $o ).
thf(tp_left_child_of,type,
left_child_of: $i > $i ).
thf(tp_n,type,
n: $i ).
thf(tp_n_left,type,
n_left: $i ).
thf(tp_n_right,type,
n_right: $i ).
thf(tp_negate,type,
negate: $i > $i ).
thf(tp_or,type,
or: $i > $i > $i ).
thf(tp_parent_of,type,
parent_of: $i > $i > $i ).
thf(tp_right_child_of,type,
right_child_of: $i > $i ).
thf(tp_siblings,type,
siblings: $i > $i > $o ).
thf(1,axiom,
! [X: $i] : ( siblings @ ( left_child_of @ X ) @ ( right_child_of @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_left_and_n_right_are_siblings) ).
thf(2,axiom,
! [X: $i] : ( contradictory @ X @ ( negate @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_contradicts_not_x) ).
thf(3,axiom,
! [X: $i] : ( contradictory @ ( negate @ X ) @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_x_contradicts_x) ).
thf(4,axiom,
! [X: $i,Y: $i,C: $i,D: $i,P: $i,Q: $i] :
( ( failure_node @ ( parent_of @ X @ Y ) @ ( or @ C @ D ) )
| ~ ( failure_node @ X @ ( or @ C @ P ) )
| ~ ( failure_node @ Y @ ( or @ D @ Q ) )
| ~ ( contradictory @ P @ Q )
| ~ ( siblings @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',make_node) ).
thf(5,axiom,
( n_right
= ( right_child_of @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_right_equals_right_child_of_n) ).
thf(6,axiom,
( n_left
= ( left_child_of @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_left_equals_left_child_of_n) ).
thf(7,axiom,
failure_node @ n_right @ ( or @ empty @ ( negate @ atom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_right_is_not_atom) ).
thf(8,axiom,
failure_node @ n_left @ ( or @ empty @ atom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_left_is_atom) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
! [Z: $i] :
~ ( failure_node @ Z @ ( or @ empty @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_is_there_an_empty_node) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [X: $i] : ( siblings @ ( left_child_of @ X ) @ ( right_child_of @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [X: $i] : ( contradictory @ X @ ( negate @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [X: $i] : ( contradictory @ ( negate @ X ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,C: $i,D: $i,P: $i,Q: $i] :
( ( failure_node @ ( parent_of @ X @ Y ) @ ( or @ C @ D ) )
| ~ ( failure_node @ X @ ( or @ C @ P ) )
| ~ ( failure_node @ Y @ ( or @ D @ Q ) )
| ~ ( contradictory @ P @ Q )
| ~ ( siblings @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( n_right
= ( right_child_of @ n ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( n_left
= ( left_child_of @ n ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( failure_node @ n_right @ ( or @ empty @ ( negate @ atom ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( failure_node @ n_left @ ( or @ empty @ atom ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [Z: $i] :
~ ( failure_node @ Z @ ( or @ empty @ empty ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i,C: $i,D: $i] :
( ( failure_node @ ( parent_of @ X @ Y ) @ ( or @ C @ D ) )
| ! [P: $i] :
( ~ ( failure_node @ X @ ( or @ C @ P ) )
| ! [Q: $i] :
( ~ ( failure_node @ Y @ ( or @ D @ Q ) )
| ~ ( contradictory @ P @ Q )
| ~ ( siblings @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(24,plain,
( ( ! [Z: $i] :
~ ( failure_node @ Z @ ( or @ empty @ empty ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(25,plain,
( ( failure_node @ n_left @ ( or @ empty @ atom ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(26,plain,
( ( failure_node @ n_right @ ( or @ empty @ ( negate @ atom ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(27,plain,
( ( n_left
= ( left_child_of @ n ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(28,plain,
( ( n_right
= ( right_child_of @ n ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,C: $i,D: $i] :
( ( failure_node @ ( parent_of @ X @ Y ) @ ( or @ C @ D ) )
| ! [P: $i] :
( ~ ( failure_node @ X @ ( or @ C @ P ) )
| ! [Q: $i] :
( ~ ( failure_node @ Y @ ( or @ D @ Q ) )
| ~ ( contradictory @ P @ Q )
| ~ ( siblings @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(30,plain,
( ( ! [X: $i] : ( contradictory @ ( negate @ X ) @ X ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(31,plain,
( ( ! [X: $i] : ( contradictory @ X @ ( negate @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(32,plain,
( ( ! [X: $i] : ( siblings @ ( left_child_of @ X ) @ ( right_child_of @ X ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(33,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(34,plain,
! [SV1: $i] :
( ( ~ ( failure_node @ SV1 @ ( or @ empty @ empty ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(35,plain,
! [SV2: $i] :
( ( ! [SY10: $i,SY11: $i,SY12: $i] :
( ( failure_node @ ( parent_of @ SV2 @ SY10 ) @ ( or @ SY11 @ SY12 ) )
| ! [SY13: $i] :
( ~ ( failure_node @ SV2 @ ( or @ SY11 @ SY13 ) )
| ! [SY14: $i] :
( ~ ( failure_node @ SY10 @ ( or @ SY12 @ SY14 ) )
| ~ ( contradictory @ SY13 @ SY14 )
| ~ ( siblings @ SV2 @ SY10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV3: $i] :
( ( contradictory @ ( negate @ SV3 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV4: $i] :
( ( contradictory @ SV4 @ ( negate @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV5: $i] :
( ( siblings @ ( left_child_of @ SV5 ) @ ( right_child_of @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV1: $i] :
( ( failure_node @ SV1 @ ( or @ empty @ empty ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SY15 @ SY16 ) )
| ! [SY17: $i] :
( ~ ( failure_node @ SV2 @ ( or @ SY15 @ SY17 ) )
| ! [SY18: $i] :
( ~ ( failure_node @ SV6 @ ( or @ SY16 @ SY18 ) )
| ~ ( contradictory @ SY17 @ SY18 )
| ~ ( siblings @ SV2 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV7: $i,SV6: $i,SV2: $i] :
( ( ! [SY19: $i] :
( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SY19 ) )
| ! [SY20: $i] :
( ~ ( failure_node @ SV2 @ ( or @ SV7 @ SY20 ) )
| ! [SY18: $i] :
( ~ ( failure_node @ SV6 @ ( or @ SY19 @ SY18 ) )
| ~ ( contradictory @ SY20 @ SY18 )
| ~ ( siblings @ SV2 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(43,plain,
! [SV8: $i,SV7: $i,SV6: $i,SV2: $i] :
( ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
| ! [SY22: $i] :
( ~ ( failure_node @ SV2 @ ( or @ SV7 @ SY22 ) )
| ! [SY23: $i] :
( ~ ( failure_node @ SV6 @ ( or @ SV8 @ SY23 ) )
| ~ ( contradictory @ SY22 @ SY23 )
| ~ ( siblings @ SV2 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV8: $i,SV7: $i,SV6: $i,SV2: $i] :
( ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
= $true )
| ( ( ! [SY22: $i] :
( ~ ( failure_node @ SV2 @ ( or @ SV7 @ SY22 ) )
| ! [SY23: $i] :
( ~ ( failure_node @ SV6 @ ( or @ SV8 @ SY23 ) )
| ~ ( contradictory @ SY22 @ SY23 )
| ~ ( siblings @ SV2 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(45,plain,
! [SV8: $i,SV6: $i,SV9: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( failure_node @ SV2 @ ( or @ SV7 @ SV9 ) )
| ! [SY24: $i] :
( ~ ( failure_node @ SV6 @ ( or @ SV8 @ SY24 ) )
| ~ ( contradictory @ SV9 @ SY24 )
| ~ ( siblings @ SV2 @ SV6 ) ) )
= $true )
| ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(46,plain,
! [SV8: $i,SV6: $i,SV9: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( failure_node @ SV2 @ ( or @ SV7 @ SV9 ) ) )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( failure_node @ SV6 @ ( or @ SV8 @ SY24 ) )
| ~ ( contradictory @ SV9 @ SY24 )
| ~ ( siblings @ SV2 @ SV6 ) ) )
= $true )
| ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(47,plain,
! [SV8: $i,SV6: $i,SV9: $i,SV7: $i,SV2: $i] :
( ( ( failure_node @ SV2 @ ( or @ SV7 @ SV9 ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( failure_node @ SV6 @ ( or @ SV8 @ SY24 ) )
| ~ ( contradictory @ SV9 @ SY24 )
| ~ ( siblings @ SV2 @ SV6 ) ) )
= $true )
| ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV7: $i,SV2: $i,SV9: $i,SV10: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( failure_node @ SV6 @ ( or @ SV8 @ SV10 ) )
| ~ ( contradictory @ SV9 @ SV10 )
| ~ ( siblings @ SV2 @ SV6 ) )
= $true )
| ( ( failure_node @ SV2 @ ( or @ SV7 @ SV9 ) )
= $false )
| ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV7: $i,SV2: $i,SV9: $i,SV10: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( failure_node @ SV6 @ ( or @ SV8 @ SV10 ) ) )
= $true )
| ( ( ~ ( contradictory @ SV9 @ SV10 )
| ~ ( siblings @ SV2 @ SV6 ) )
= $true )
| ( ( failure_node @ SV2 @ ( or @ SV7 @ SV9 ) )
= $false )
| ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV7: $i,SV2: $i,SV9: $i,SV10: $i,SV8: $i,SV6: $i] :
( ( ( failure_node @ SV6 @ ( or @ SV8 @ SV10 ) )
= $false )
| ( ( ~ ( contradictory @ SV9 @ SV10 )
| ~ ( siblings @ SV2 @ SV6 ) )
= $true )
| ( ( failure_node @ SV2 @ ( or @ SV7 @ SV9 ) )
= $false )
| ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(51,plain,
! [SV7: $i,SV8: $i,SV6: $i,SV2: $i,SV10: $i,SV9: $i] :
( ( ( ~ ( contradictory @ SV9 @ SV10 ) )
= $true )
| ( ( ~ ( siblings @ SV2 @ SV6 ) )
= $true )
| ( ( failure_node @ SV6 @ ( or @ SV8 @ SV10 ) )
= $false )
| ( ( failure_node @ SV2 @ ( or @ SV7 @ SV9 ) )
= $false )
| ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(52,plain,
! [SV7: $i,SV8: $i,SV6: $i,SV2: $i,SV10: $i,SV9: $i] :
( ( ( contradictory @ SV9 @ SV10 )
= $false )
| ( ( ~ ( siblings @ SV2 @ SV6 ) )
= $true )
| ( ( failure_node @ SV6 @ ( or @ SV8 @ SV10 ) )
= $false )
| ( ( failure_node @ SV2 @ ( or @ SV7 @ SV9 ) )
= $false )
| ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(53,plain,
! [SV7: $i,SV8: $i,SV10: $i,SV9: $i,SV6: $i,SV2: $i] :
( ( ( siblings @ SV2 @ SV6 )
= $false )
| ( ( contradictory @ SV9 @ SV10 )
= $false )
| ( ( failure_node @ SV6 @ ( or @ SV8 @ SV10 ) )
= $false )
| ( ( failure_node @ SV2 @ ( or @ SV7 @ SV9 ) )
= $false )
| ( ( failure_node @ ( parent_of @ SV2 @ SV6 ) @ ( or @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(54,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,53,40,39,38,37,36,28,27,26]) ).
thf(55,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COM004-1 : TPTP v8.1.0. Released v1.1.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n024.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 16 19:38:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.36
% 0.20/0.36 No.of.Axioms: 9
% 0.20/0.36
% 0.20/0.36 Length.of.Defs: 0
% 0.20/0.36
% 0.20/0.36 Contains.Choice.Funs: false
% 0.20/0.36 (rf:0,axioms:9,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:11,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.20/0.41
% 0.20/0.41 ********************************
% 0.20/0.41 * All subproblems solved! *
% 0.20/0.41 ********************************
% 0.20/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:54,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.41
% 0.20/0.41 %**** Beginning of derivation protocol ****
% 0.20/0.41 % SZS output start CNFRefutation
% See solution above
% 0.20/0.41
% 0.20/0.41 %**** End of derivation protocol ****
% 0.20/0.41 %**** no. of clauses in derivation: 55 ****
% 0.20/0.41 %**** clause counter: 54 ****
% 0.20/0.41
% 0.20/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:54,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------