TSTP Solution File: NUM016-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM016-2 : 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 : n003.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 11:46:23 EDT 2022
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 39 unt; 6 typ; 0 def)
% Number of atoms : 227 ( 61 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 285 ( 37 ~; 48 |; 0 &; 200 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 ^ 64 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_divides,type,
divides: $i > $i > $o ).
thf(tp_factorial_plus_one,type,
factorial_plus_one: $i > $i ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_prime,type,
prime: $i > $o ).
thf(tp_prime_divisor,type,
prime_divisor: $i > $i ).
thf(1,axiom,
! [X: $i] :
( ( prime @ X )
| ( less @ ( prime_divisor @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_prime_divisors) ).
thf(2,axiom,
! [X: $i] :
( ( prime @ X )
| ( prime @ ( prime_divisor @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_divsiors) ).
thf(3,axiom,
! [X: $i] :
( ( prime @ X )
| ( divides @ ( prime_divisor @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',division_by_prime_divisor) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ~ ( divides @ X @ ( factorial_plus_one @ Y ) )
| ( less @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_is_smaller) ).
thf(5,axiom,
! [X: $i] : ( less @ X @ ( factorial_plus_one @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ~ ( less @ X @ Y )
| ~ ( less @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_are_different) ).
thf(7,axiom,
! [X: $i] :
~ ( less @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
thf(8,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(9,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,negated_conjecture,
! [X: $i] :
( ~ ( prime @ X )
| ~ ( less @ a @ X )
| ( less @ ( factorial_plus_one @ a ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
thf(11,plain,
$false = $false,
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [X: $i] :
( ( prime @ X )
| ( less @ ( prime_divisor @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [X: $i] :
( ( prime @ X )
| ( prime @ ( prime_divisor @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [X: $i] :
( ( prime @ X )
| ( divides @ ( prime_divisor @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( divides @ X @ ( factorial_plus_one @ Y ) )
| ( less @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [X: $i] : ( less @ X @ ( factorial_plus_one @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less @ X @ Y )
| ~ ( less @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [X: $i] :
~ ( less @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [X: $i] :
( ~ ( prime @ X )
| ~ ( less @ a @ X )
| ( less @ ( factorial_plus_one @ a ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( less @ ( prime_divisor @ X ) @ X )
| ( prime @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(22,plain,
( ( ! [X: $i] :
( ( divides @ ( prime_divisor @ X ) @ X )
| ( prime @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(23,plain,
( ( ! [X: $i] :
( ~ ( prime @ X )
| ~ ( less @ a @ X )
| ( less @ ( factorial_plus_one @ a ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [X: $i] :
~ ( less @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less @ X @ Y )
| ~ ( less @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ! [X: $i] : ( less @ X @ ( factorial_plus_one @ X ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( divides @ X @ ( factorial_plus_one @ Y ) )
| ( less @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( divides @ ( prime_divisor @ X ) @ X )
| ( prime @ X ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( prime @ X )
| ( prime @ ( prime_divisor @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(30,plain,
( ( ! [X: $i] :
( ( less @ ( prime_divisor @ X ) @ X )
| ( prime @ X ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(31,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(32,plain,
! [SV1: $i] :
( ( ~ ( prime @ SV1 )
| ~ ( less @ a @ SV1 )
| ( less @ ( factorial_plus_one @ a ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(33,plain,
! [SV2: $i] :
( ( ~ ( less @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(34,plain,
! [SV3: $i] :
( ( ! [SY10: $i] :
( ~ ( less @ SV3 @ SY10 )
| ~ ( less @ SY10 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(35,plain,
! [SV4: $i] :
( ( less @ SV4 @ ( factorial_plus_one @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV5: $i] :
( ( ! [SY11: $i] :
( ~ ( divides @ SV5 @ ( factorial_plus_one @ SY11 ) )
| ( less @ SY11 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV6: $i] :
( ( ( divides @ ( prime_divisor @ SV6 ) @ SV6 )
| ( prime @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV7: $i] :
( ( ( prime @ SV7 )
| ( prime @ ( prime_divisor @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
! [SV8: $i] :
( ( ( less @ ( prime_divisor @ SV8 ) @ SV8 )
| ( prime @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV1: $i] :
( ( ( ~ ( prime @ SV1 ) )
= $true )
| ( ( ~ ( less @ a @ SV1 )
| ( less @ ( factorial_plus_one @ a ) @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV2: $i] :
( ( less @ SV2 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(43,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ( less @ SV3 @ SV9 )
| ~ ( less @ SV9 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(44,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( divides @ SV5 @ ( factorial_plus_one @ SV10 ) )
| ( less @ SV10 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV6: $i] :
( ( ( divides @ ( prime_divisor @ SV6 ) @ SV6 )
= $true )
| ( ( prime @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV7: $i] :
( ( ( prime @ SV7 )
= $true )
| ( ( prime @ ( prime_divisor @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV8: $i] :
( ( ( less @ ( prime_divisor @ SV8 ) @ SV8 )
= $true )
| ( ( prime @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV1: $i] :
( ( ( prime @ SV1 )
= $false )
| ( ( ~ ( less @ a @ SV1 )
| ( less @ ( factorial_plus_one @ a ) @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( less @ SV3 @ SV9 ) )
= $true )
| ( ( ~ ( less @ SV9 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( divides @ SV5 @ ( factorial_plus_one @ SV10 ) ) )
= $true )
| ( ( less @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV1: $i] :
( ( ( ~ ( less @ a @ SV1 ) )
= $true )
| ( ( less @ ( factorial_plus_one @ a ) @ SV1 )
= $true )
| ( ( prime @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV9: $i,SV3: $i] :
( ( ( less @ SV3 @ SV9 )
= $false )
| ( ( ~ ( less @ SV9 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV10: $i,SV5: $i] :
( ( ( divides @ SV5 @ ( factorial_plus_one @ SV10 ) )
= $false )
| ( ( less @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV1: $i] :
( ( ( less @ a @ SV1 )
= $false )
| ( ( less @ ( factorial_plus_one @ a ) @ SV1 )
= $true )
| ( ( prime @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV3: $i,SV9: $i] :
( ( ( less @ SV9 @ SV3 )
= $false )
| ( ( less @ SV3 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(56,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,55,54,53,47,46,45,42,40]) ).
thf(57,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jul 6 16:27:11 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 8
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.36 (rf:0,axioms:8,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:10,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.14/0.39
% 0.14/0.39 ********************************
% 0.14/0.39 * All subproblems solved! *
% 0.14/0.39 ********************************
% 0.14/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.39
% 0.14/0.39 %**** Beginning of derivation protocol ****
% 0.14/0.39 % SZS output start CNFRefutation
% See solution above
% 0.14/0.39
% 0.14/0.39 %**** End of derivation protocol ****
% 0.14/0.39 %**** no. of clauses in derivation: 57 ****
% 0.14/0.39 %**** clause counter: 56 ****
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------