TSTP Solution File: NUM419^1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM419^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n010.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 11:49:33 EDT 2022
% Result : Theorem 101.50s 101.73s
% Output : CNFRefutation 101.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 43
% Syntax : Number of formulae : 53 ( 25 unt; 28 typ; 14 def)
% Number of atoms : 43 ( 32 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 136 ( 4 ~; 0 |; 0 &; 132 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 271 ( 271 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 2 con; 0-4 aty)
% Number of variables : 70 ( 61 ^ 5 !; 4 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_eight,type,
eight: ( $i > $i ) > $i > $i ).
thf(tp_five,type,
five: ( $i > $i ) > $i > $i ).
thf(tp_four,type,
four: ( $i > $i ) > $i > $i ).
thf(tp_mult,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_nine,type,
nine: ( $i > $i ) > $i > $i ).
thf(tp_one,type,
one: ( $i > $i ) > $i > $i ).
thf(tp_plus,type,
plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_sK10_E,type,
sK10_E: ( ( $i > $i ) > $i > $i ) > $i ).
thf(tp_sK11_E,type,
sK11_E: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > ( $i > $i ) > $i > $i ) > $i > $i ).
thf(tp_sK12_E,type,
sK12_E: ( ( $i > $i ) > $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i ).
thf(tp_sK13_E,type,
sK13_E: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > ( $i > $i ) > $i > ( $i > $i ) > $i > $i ) > $i > $i ).
thf(tp_sK14_E,type,
sK14_E: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > ( $i > $i ) > $i > ( $i > $i ) > $i > $i ) > $i ).
thf(tp_sK1_SV2,type,
sK1_SV2: ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(tp_sK2_SV3,type,
sK2_SV3: ( ( $i > $i ) > $i > $i ) > $i ).
thf(tp_sK3_E,type,
sK3_E: ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(tp_sK4_E,type,
sK4_E: ( ( $i > $i ) > $i > $i ) > $i ).
thf(tp_sK5_E,type,
sK5_E: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > ( $i > $i ) > $i > $i ) > $i > $i ).
thf(tp_sK6_E,type,
sK6_E: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > ( $i > $i ) > $i > $i ) > $i ).
thf(tp_sK7_E,type,
sK7_E: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > ( $i > $i ) > $i > $i ) > $i > $i ).
thf(tp_sK8_E,type,
sK8_E: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > ( $i > $i ) > $i > $i ) > $i ).
thf(tp_sK9_E,type,
sK9_E: ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(tp_seven,type,
seven: ( $i > $i ) > $i > $i ).
thf(tp_six,type,
six: ( $i > $i ) > $i > $i ).
thf(tp_succ,type,
succ: ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_ten,type,
ten: ( $i > $i ) > $i > $i ).
thf(tp_three,type,
three: ( $i > $i ) > $i > $i ).
thf(tp_two,type,
two: ( $i > $i ) > $i > $i ).
thf(tp_zero,type,
zero: ( $i > $i ) > $i > $i ).
thf(eight,definition,
( eight
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eight) ).
thf(five,definition,
( five
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',five) ).
thf(four,definition,
( four
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',four) ).
thf(mult,definition,
( mult
= ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ ( N @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mult) ).
thf(nine,definition,
( nine
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nine) ).
thf(one,definition,
( one
= ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one) ).
thf(plus,definition,
( plus
= ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ X @ ( N @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus) ).
thf(seven,definition,
( seven
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',seven) ).
thf(six,definition,
( six
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',six) ).
thf(succ,definition,
( succ
= ( ^ [N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( X @ ( N @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ) ).
thf(ten,definition,
( ten
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ten) ).
thf(three,definition,
( three
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',three) ).
thf(two,definition,
( two
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two) ).
thf(zero,definition,
( zero
= ( ^ [X: $i > $i,Y: $i] : Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero) ).
thf(1,conjecture,
? [N: ( $i > $i ) > $i > $i] :
( ( plus @ N @ three )
= four ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ? [N: ( $i > $i ) > $i > $i] :
( ( plus @ N @ three )
= four ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [SY541: ( $i > $i ) > $i > $i] :
( ( ^ [SY545: $i > $i,SY546: $i] : ( SY541 @ SY545 @ ( SY545 @ ( SY545 @ ( SY545 @ SY546 ) ) ) ) )
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,eight,five,four,mult,nine,one,plus,seven,six,succ,ten,three,two,zero]) ).
thf(4,plain,
( ( ~ ? [SY541: ( $i > $i ) > $i > $i] :
( ( ^ [SY545: $i > $i,SY546: $i] : ( SY541 @ SY545 @ ( SY545 @ ( SY545 @ ( SY545 @ SY546 ) ) ) ) )
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY541: ( $i > $i ) > $i > $i] :
( ( ^ [SY545: $i > $i,SY546: $i] : ( SY541 @ SY545 @ ( SY545 @ ( SY545 @ ( SY545 @ SY546 ) ) ) ) )
!= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY541: ( $i > $i ) > $i > $i] :
( ( ^ [SY545: $i > $i,SY546: $i] : ( SY541 @ SY545 @ ( SY545 @ ( SY545 @ ( SY545 @ SY546 ) ) ) ) )
!= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ( ( ^ [SY553: $i > $i,SY554: $i] : ( SV1 @ SY553 @ ( SY553 @ ( SY553 @ ( SY553 @ SY554 ) ) ) ) )
!= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ( ^ [SY553: $i > $i,SY554: $i] : ( SV1 @ SY553 @ ( SY553 @ ( SY553 @ ( SY553 @ SY554 ) ) ) ) )
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(10,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ( ^ [SY553: $i > $i,SY554: $i] : ( SV1 @ SY553 @ ( SY553 @ ( SY553 @ ( SY553 @ SY554 ) ) ) ) )
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[8]) ).
thf(18,plain,
$false = $true,
inference(extuni,[status(esa)],[10:[bind(SV1,$thf( ^ [SX0: $i > $i] : ^ [SX1: $i] : ( SX0 @ SX1 ) ))]]) ).
thf(19,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM419^1 : TPTP v8.1.0. Released v3.6.0.
% 0.12/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n010.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 : Tue Jul 5 22:06:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.34
% 0.18/0.34 No.of.Axioms: 0
% 0.18/0.34
% 0.18/0.34 Length.of.Defs: 2009
% 0.18/0.34
% 0.18/0.34 Contains.Choice.Funs: false
% 0.18/0.34 (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)eprover: CPU time limit exceeded, terminating
% 25.20/25.42 .......
% 75.11/75.34 (rf:0,axioms:0,ps:3,u:3,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).eprover: CPU time limit exceeded, terminating
% 100.15/100.42 ..
% 101.50/101.73
% 101.50/101.73 ********************************
% 101.50/101.73 * All subproblems solved! *
% 101.50/101.73 ********************************
% 101.50/101.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:3,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:1,translation:fof_full)
% 101.50/101.73
% 101.50/101.73 %**** Beginning of derivation protocol ****
% 101.50/101.73 % SZS output start CNFRefutation
% See solution above
% 101.50/101.73
% 101.50/101.73 %**** End of derivation protocol ****
% 101.50/101.73 %**** no. of clauses in derivation: 11 ****
% 101.50/101.73 %**** clause counter: 18 ****
% 101.50/101.73
% 101.50/101.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:3,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------