TSTP Solution File: COM001-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : COM001-1 : 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 : n013.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 01:28:29 EDT 2022
% Result : Unsatisfiable 0.22s 0.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of formulae : 83 ( 49 unt; 15 typ; 0 def)
% Number of atoms : 280 ( 76 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 404 ( 57 ~; 60 |; 0 &; 287 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 107 ( 0 ^ 107 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_equal_function,type,
equal_function: $i > $i > $i ).
thf(tp_follows,type,
follows: $i > $i > $o ).
thf(tp_goto,type,
goto: $i > $i ).
thf(tp_has,type,
has: $i > $i > $o ).
thf(tp_ifthen,type,
ifthen: $i > $i > $i ).
thf(tp_labels,type,
labels: $i > $i > $o ).
thf(tp_loop,type,
loop: $i ).
thf(tp_n,type,
n: $i ).
thf(tp_out,type,
out: $i ).
thf(tp_p3,type,
p3: $i ).
thf(tp_p4,type,
p4: $i ).
thf(tp_p5,type,
p5: $i ).
thf(tp_p8,type,
p8: $i ).
thf(tp_register_j,type,
register_j: $i ).
thf(tp_succeeds,type,
succeeds: $i > $i > $o ).
thf(1,axiom,
! [Goal_state: $i,Start_state: $i,Condition: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ~ ( has @ Start_state @ ( ifthen @ Condition @ Goal_state ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conditional_success) ).
thf(2,axiom,
! [Goal_state: $i,Start_state: $i,Label: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ~ ( has @ Start_state @ ( goto @ Label ) )
| ~ ( labels @ Label @ Goal_state ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goto_success) ).
thf(3,axiom,
! [Goal_state: $i,Start_state: $i,Intermediate_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ~ ( succeeds @ Goal_state @ Intermediate_state )
| ~ ( succeeds @ Intermediate_state @ Start_state ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_success) ).
thf(4,axiom,
! [Goal_state: $i,Start_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ~ ( follows @ Goal_state @ Start_state ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',direct_success) ).
thf(5,axiom,
has @ p8 @ ( goto @ loop ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',state_8) ).
thf(6,axiom,
follows @ p8 @ p3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transition_3_to_8) ).
thf(7,axiom,
follows @ p5 @ p4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transition_4_to_5) ).
thf(8,axiom,
has @ p4 @ ( goto @ out ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',state_4) ).
thf(9,axiom,
has @ p3 @ ( ifthen @ ( equal_function @ register_j @ n ) @ p4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',state_3) ).
thf(10,axiom,
labels @ loop @ p3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',label_state_3) ).
thf(11,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(12,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,negated_conjecture,
~ ( succeeds @ p3 @ p3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_loop_through_p3) ).
thf(14,plain,
$false = $false,
inference(unfold_def,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [Goal_state: $i,Start_state: $i,Condition: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ~ ( has @ Start_state @ ( ifthen @ Condition @ Goal_state ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [Goal_state: $i,Start_state: $i,Label: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ~ ( has @ Start_state @ ( goto @ Label ) )
| ~ ( labels @ Label @ Goal_state ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [Goal_state: $i,Start_state: $i,Intermediate_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ~ ( succeeds @ Goal_state @ Intermediate_state )
| ~ ( succeeds @ Intermediate_state @ Start_state ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [Goal_state: $i,Start_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ~ ( follows @ Goal_state @ Start_state ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( has @ p8 @ ( goto @ loop ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( follows @ p8 @ p3 )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( follows @ p5 @ p4 )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( has @ p4 @ ( goto @ out ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( has @ p3 @ ( ifthen @ ( equal_function @ register_j @ n ) @ p4 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( labels @ loop @ p3 )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ~ ( succeeds @ p3 @ p3 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(26,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [Goal_state: $i,Start_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ! [Condition: $i] :
~ ( has @ Start_state @ ( ifthen @ Condition @ Goal_state ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(28,plain,
( ( ! [Goal_state: $i,Start_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ! [Label: $i] :
( ~ ( has @ Start_state @ ( goto @ Label ) )
| ~ ( labels @ Label @ Goal_state ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(29,plain,
( ( ! [Goal_state: $i,Start_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ! [Intermediate_state: $i] :
( ~ ( succeeds @ Goal_state @ Intermediate_state )
| ~ ( succeeds @ Intermediate_state @ Start_state ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(30,plain,
( ( ~ ( succeeds @ p3 @ p3 ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(31,plain,
( ( labels @ loop @ p3 )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(32,plain,
( ( has @ p3 @ ( ifthen @ ( equal_function @ register_j @ n ) @ p4 ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(33,plain,
( ( has @ p4 @ ( goto @ out ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(34,plain,
( ( follows @ p5 @ p4 )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(35,plain,
( ( follows @ p8 @ p3 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(36,plain,
( ( has @ p8 @ ( goto @ loop ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(37,plain,
( ( ! [Goal_state: $i,Start_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ~ ( follows @ Goal_state @ Start_state ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(38,plain,
( ( ! [Goal_state: $i,Start_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ! [Intermediate_state: $i] :
( ~ ( succeeds @ Goal_state @ Intermediate_state )
| ~ ( succeeds @ Intermediate_state @ Start_state ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(39,plain,
( ( ! [Goal_state: $i,Start_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ! [Label: $i] :
( ~ ( has @ Start_state @ ( goto @ Label ) )
| ~ ( labels @ Label @ Goal_state ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(40,plain,
( ( ! [Goal_state: $i,Start_state: $i] :
( ( succeeds @ Goal_state @ Start_state )
| ! [Condition: $i] :
~ ( has @ Start_state @ ( ifthen @ Condition @ Goal_state ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(41,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(42,plain,
( ( succeeds @ p3 @ p3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(43,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
( ( succeeds @ SV1 @ SY11 )
| ~ ( follows @ SV1 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
( ( succeeds @ SV2 @ SY12 )
| ! [SY13: $i] :
( ~ ( succeeds @ SV2 @ SY13 )
| ~ ( succeeds @ SY13 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV3: $i] :
( ( ! [SY14: $i] :
( ( succeeds @ SV3 @ SY14 )
| ! [SY15: $i] :
( ~ ( has @ SY14 @ ( goto @ SY15 ) )
| ~ ( labels @ SY15 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV4: $i] :
( ( ! [SY16: $i] :
( ( succeeds @ SV4 @ SY16 )
| ! [SY17: $i] :
~ ( has @ SY16 @ ( ifthen @ SY17 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV5: $i,SV1: $i] :
( ( ( succeeds @ SV1 @ SV5 )
| ~ ( follows @ SV1 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV6: $i,SV2: $i] :
( ( ( succeeds @ SV2 @ SV6 )
| ! [SY18: $i] :
( ~ ( succeeds @ SV2 @ SY18 )
| ~ ( succeeds @ SY18 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV7: $i,SV3: $i] :
( ( ( succeeds @ SV3 @ SV7 )
| ! [SY19: $i] :
( ~ ( has @ SV7 @ ( goto @ SY19 ) )
| ~ ( labels @ SY19 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV8: $i,SV4: $i] :
( ( ( succeeds @ SV4 @ SV8 )
| ! [SY20: $i] :
~ ( has @ SV8 @ ( ifthen @ SY20 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV5: $i,SV1: $i] :
( ( ( succeeds @ SV1 @ SV5 )
= $true )
| ( ( ~ ( follows @ SV1 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV6: $i,SV2: $i] :
( ( ( succeeds @ SV2 @ SV6 )
= $true )
| ( ( ! [SY18: $i] :
( ~ ( succeeds @ SV2 @ SY18 )
| ~ ( succeeds @ SY18 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV7: $i,SV3: $i] :
( ( ( succeeds @ SV3 @ SV7 )
= $true )
| ( ( ! [SY19: $i] :
( ~ ( has @ SV7 @ ( goto @ SY19 ) )
| ~ ( labels @ SY19 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV8: $i,SV4: $i] :
( ( ( succeeds @ SV4 @ SV8 )
= $true )
| ( ( ! [SY20: $i] :
~ ( has @ SV8 @ ( ifthen @ SY20 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV5: $i,SV1: $i] :
( ( ( follows @ SV1 @ SV5 )
= $false )
| ( ( succeeds @ SV1 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV6: $i,SV9: $i,SV2: $i] :
( ( ( ~ ( succeeds @ SV2 @ SV9 )
| ~ ( succeeds @ SV9 @ SV6 ) )
= $true )
| ( ( succeeds @ SV2 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV3: $i,SV10: $i,SV7: $i] :
( ( ( ~ ( has @ SV7 @ ( goto @ SV10 ) )
| ~ ( labels @ SV10 @ SV3 ) )
= $true )
| ( ( succeeds @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV4: $i,SV11: $i,SV8: $i] :
( ( ( ~ ( has @ SV8 @ ( ifthen @ SV11 @ SV4 ) ) )
= $true )
| ( ( succeeds @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV6: $i,SV9: $i,SV2: $i] :
( ( ( ~ ( succeeds @ SV2 @ SV9 ) )
= $true )
| ( ( ~ ( succeeds @ SV9 @ SV6 ) )
= $true )
| ( ( succeeds @ SV2 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV3: $i,SV10: $i,SV7: $i] :
( ( ( ~ ( has @ SV7 @ ( goto @ SV10 ) ) )
= $true )
| ( ( ~ ( labels @ SV10 @ SV3 ) )
= $true )
| ( ( succeeds @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV4: $i,SV11: $i,SV8: $i] :
( ( ( has @ SV8 @ ( ifthen @ SV11 @ SV4 ) )
= $false )
| ( ( succeeds @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV6: $i,SV9: $i,SV2: $i] :
( ( ( succeeds @ SV2 @ SV9 )
= $false )
| ( ( ~ ( succeeds @ SV9 @ SV6 ) )
= $true )
| ( ( succeeds @ SV2 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV3: $i,SV10: $i,SV7: $i] :
( ( ( has @ SV7 @ ( goto @ SV10 ) )
= $false )
| ( ( ~ ( labels @ SV10 @ SV3 ) )
= $true )
| ( ( succeeds @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV2: $i,SV6: $i,SV9: $i] :
( ( ( succeeds @ SV9 @ SV6 )
= $false )
| ( ( succeeds @ SV2 @ SV9 )
= $false )
| ( ( succeeds @ SV2 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV7: $i,SV3: $i,SV10: $i] :
( ( ( labels @ SV10 @ SV3 )
= $false )
| ( ( has @ SV7 @ ( goto @ SV10 ) )
= $false )
| ( ( succeeds @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,66,65,62,56,47,42,36,35,34,33,32]) ).
thf(68,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : COM001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.15 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 600
% 0.16/0.36 % DateTime : Thu Jun 16 16:55:29 EDT 2022
% 0.16/0.36 % CPUTime :
% 0.22/0.37
% 0.22/0.37 No.of.Axioms: 11
% 0.22/0.37
% 0.22/0.37 Length.of.Defs: 0
% 0.22/0.37
% 0.22/0.37 Contains.Choice.Funs: false
% 0.22/0.37 (rf:0,axioms:11,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:13,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.22/0.41
% 0.22/0.41 ********************************
% 0.22/0.41 * All subproblems solved! *
% 0.22/0.41 ********************************
% 0.22/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,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:67,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.22/0.41
% 0.22/0.41 %**** Beginning of derivation protocol ****
% 0.22/0.41 % SZS output start CNFRefutation
% See solution above
% 0.22/0.41
% 0.22/0.41 %**** End of derivation protocol ****
% 0.22/0.41 %**** no. of clauses in derivation: 68 ****
% 0.22/0.41 %**** clause counter: 67 ****
% 0.22/0.41
% 0.22/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,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:67,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------