TSTP Solution File: ROB011-1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ROB011-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:54:06 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 62 ( 46 unt; 9 typ; 0 def)
% Number of atoms : 161 ( 83 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 304 ( 17 ~; 14 |; 0 &; 273 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 64 ( 0 ^ 64 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_negate,type,
negate: $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_positive_integer,type,
positive_integer: $i > $o ).
thf(tp_successor,type,
successor: $i > $i ).
thf(1,axiom,
! [X: $i] :
( ~ ( positive_integer @ X )
| ( positive_integer @ ( successor @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',next_integer) ).
thf(2,axiom,
positive_integer @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one) ).
thf(3,axiom,
! [X: $i,V: $i] :
( ~ ( positive_integer @ X )
| ( ( multiply @ ( successor @ V ) @ X )
= ( add @ X @ ( multiply @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_by_adding) ).
thf(4,axiom,
! [X: $i] :
( ( multiply @ one @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_times_x) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( negate @ ( add @ ( negate @ ( add @ X @ Y ) ) @ ( negate @ ( add @ X @ ( negate @ Y ) ) ) ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',robbins_axiom) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( add @ ( add @ X @ Y ) @ Z )
= ( add @ X @ ( add @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(8,axiom,
( ( negate @ ( add @ a @ ( negate @ b ) ) )
= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
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,
( negate @ ( add @ a @ ( negate @ ( add @ b @ ( multiply @ one @ ( add @ a @ c ) ) ) ) ) )
!= c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_base_step) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [X: $i] :
( ~ ( positive_integer @ X )
| ( positive_integer @ ( successor @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( positive_integer @ one )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [X: $i,V: $i] :
( ~ ( positive_integer @ X )
| ( ( multiply @ ( successor @ V ) @ X )
= ( add @ X @ ( multiply @ V @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( multiply @ one @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ( negate @ ( add @ ( negate @ ( add @ X @ Y ) ) @ ( negate @ ( add @ X @ ( negate @ Y ) ) ) ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ ( add @ X @ Y ) @ Z )
= ( add @ X @ ( add @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ( negate @ ( add @ a @ ( negate @ b ) ) )
= c )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ( ( negate @ ( add @ a @ ( negate @ ( add @ b @ ( multiply @ one @ ( add @ a @ c ) ) ) ) ) )
!= c ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [X: $i] :
( ~ ( positive_integer @ X )
| ! [V: $i] :
( ( multiply @ ( successor @ V ) @ X )
= ( add @ X @ ( multiply @ V @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(24,plain,
( ( ( ( negate @ ( add @ a @ ( negate @ ( add @ b @ ( multiply @ one @ ( add @ a @ c ) ) ) ) ) )
!= c ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(25,plain,
( ( ( ( negate @ ( add @ a @ ( negate @ ( add @ b @ ( multiply @ one @ ( add @ a @ c ) ) ) ) ) )
!= c ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(26,plain,
( ( ( negate @ ( add @ a @ ( negate @ b ) ) )
= c )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ ( add @ X @ Y ) @ Z )
= ( add @ X @ ( add @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( negate @ ( add @ ( negate @ ( add @ X @ Y ) ) @ ( negate @ ( add @ X @ ( negate @ Y ) ) ) ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(30,plain,
( ( ! [X: $i] :
( ( multiply @ one @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [X: $i] :
( ~ ( positive_integer @ X )
| ! [V: $i] :
( ( multiply @ ( successor @ V ) @ X )
= ( add @ X @ ( multiply @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(32,plain,
( ( positive_integer @ one )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(33,plain,
( ( ! [X: $i] :
( ~ ( positive_integer @ X )
| ( positive_integer @ ( successor @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(34,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( ( negate @ ( add @ a @ ( negate @ ( add @ b @ ( multiply @ one @ ( add @ a @ c ) ) ) ) ) )
= c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
( ( add @ SV1 @ SY11 )
= ( add @ SY11 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV2: $i] :
( ( ! [SY12: $i,SY13: $i] :
( ( add @ ( add @ SV2 @ SY12 ) @ SY13 )
= ( add @ SV2 @ ( add @ SY12 @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV3: $i] :
( ( ! [SY14: $i] :
( ( negate @ ( add @ ( negate @ ( add @ SV3 @ SY14 ) ) @ ( negate @ ( add @ SV3 @ ( negate @ SY14 ) ) ) ) )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
! [SV4: $i] :
( ( ( multiply @ one @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV5: $i] :
( ( ~ ( positive_integer @ SV5 )
| ! [SY15: $i] :
( ( multiply @ ( successor @ SY15 ) @ SV5 )
= ( add @ SV5 @ ( multiply @ SY15 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV6: $i] :
( ( ~ ( positive_integer @ SV6 )
| ( positive_integer @ ( successor @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV7: $i,SV1: $i] :
( ( ( add @ SV1 @ SV7 )
= ( add @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV8: $i,SV2: $i] :
( ( ! [SY16: $i] :
( ( add @ ( add @ SV2 @ SV8 ) @ SY16 )
= ( add @ SV2 @ ( add @ SV8 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV9: $i,SV3: $i] :
( ( ( negate @ ( add @ ( negate @ ( add @ SV3 @ SV9 ) ) @ ( negate @ ( add @ SV3 @ ( negate @ SV9 ) ) ) ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV5: $i] :
( ( ( ~ ( positive_integer @ SV5 ) )
= $true )
| ( ( ! [SY15: $i] :
( ( multiply @ ( successor @ SY15 ) @ SV5 )
= ( add @ SV5 @ ( multiply @ SY15 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV6: $i] :
( ( ( ~ ( positive_integer @ SV6 ) )
= $true )
| ( ( positive_integer @ ( successor @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV10: $i,SV8: $i,SV2: $i] :
( ( ( add @ ( add @ SV2 @ SV8 ) @ SV10 )
= ( add @ SV2 @ ( add @ SV8 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV5: $i] :
( ( ( positive_integer @ SV5 )
= $false )
| ( ( ! [SY15: $i] :
( ( multiply @ ( successor @ SY15 ) @ SV5 )
= ( add @ SV5 @ ( multiply @ SY15 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV6: $i] :
( ( ( positive_integer @ SV6 )
= $false )
| ( ( positive_integer @ ( successor @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV5: $i,SV11: $i] :
( ( ( ( multiply @ ( successor @ SV11 ) @ SV5 )
= ( add @ SV5 @ ( multiply @ SV11 @ SV5 ) ) )
= $true )
| ( ( positive_integer @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(52,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,51,50,48,45,43,42,39,35,32]) ).
thf(53,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ROB011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n027.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 9 16:19:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 9
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (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)..
% 0.20/0.42
% 0.20/0.42 ********************************
% 0.20/0.42 * All subproblems solved! *
% 0.20/0.42 ********************************
% 0.20/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox/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:52,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.42
% 0.20/0.42 %**** Beginning of derivation protocol ****
% 0.20/0.42 % SZS output start CNFRefutation
% See solution above
% 0.20/0.42
% 0.20/0.42 %**** End of derivation protocol ****
% 0.20/0.42 %**** no. of clauses in derivation: 53 ****
% 0.20/0.42 %**** clause counter: 52 ****
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox/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:52,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------