TSTP Solution File: NUM283-1.005 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM283-1.005 : 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 : n004.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 11:48:01 EDT 2022
% Result : Unsatisfiable 9.55s 9.73s
% Output : CNFRefutation 9.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 40 unt; 5 typ; 0 def)
% Number of atoms : 233 ( 62 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 458 ( 49 ~; 54 |; 0 &; 355 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 118 ( 0 ^ 118 !; 0 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_factorial,type,
factorial: $i > $i > $o ).
thf(tp_n0,type,
n0: $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_sum,type,
sum: $i > $i > $i > $o ).
thf(1,axiom,
! [X: $i,Z: $i,Y: $i] :
( ~ ( factorial @ X @ Z )
| ~ ( product @ ( s @ X ) @ Z @ Y )
| ( factorial @ ( s @ X ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',factorial) ).
thf(2,axiom,
factorial @ n0 @ ( s @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',factorial_0) ).
thf(3,axiom,
! [R: $i,Y: $i,Z: $i,X: $i] :
( ~ ( sum @ R @ Y @ Z )
| ~ ( product @ X @ Y @ R )
| ( product @ ( s @ X ) @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).
thf(4,axiom,
! [X: $i] : ( product @ ( s @ n0 ) @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times1) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ X @ ( s @ Y ) @ ( s @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add) ).
thf(6,axiom,
! [X: $i] : ( sum @ X @ n0 @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_0) ).
thf(7,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(8,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,negated_conjecture,
! [Result: $i] :
~ ( factorial @ ( s @ ( s @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) @ Result ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_factorial) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ~ ( factorial @ X @ Z )
| ~ ( product @ ( s @ X ) @ Z @ Y )
| ( factorial @ ( s @ X ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( factorial @ n0 @ ( s @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [R: $i,Y: $i,Z: $i,X: $i] :
( ~ ( sum @ R @ Y @ Z )
| ~ ( product @ X @ Y @ R )
| ( product @ ( s @ X ) @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [X: $i] : ( product @ ( s @ n0 ) @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ X @ ( s @ Y ) @ ( s @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [X: $i] : ( sum @ X @ n0 @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ! [Result: $i] :
~ ( factorial @ ( s @ ( s @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) @ Result ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [X: $i,Z: $i] :
( ~ ( factorial @ X @ Z )
| ! [Y: $i] :
( ~ ( product @ ( s @ X ) @ Z @ Y )
| ( factorial @ ( s @ X ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(20,plain,
( ( ! [R: $i,Y: $i,Z: $i] :
( ~ ( sum @ R @ Y @ Z )
| ! [X: $i] :
( ~ ( product @ X @ Y @ R )
| ( product @ ( s @ X ) @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(21,plain,
( ( ! [Result: $i] :
~ ( factorial @ ( s @ ( s @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) @ Result ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(22,plain,
( ( ! [X: $i] : ( sum @ X @ n0 @ X ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ X @ ( s @ Y ) @ ( s @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(24,plain,
( ( ! [X: $i] : ( product @ ( s @ n0 ) @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(25,plain,
( ( ! [R: $i,Y: $i,Z: $i] :
( ~ ( sum @ R @ Y @ Z )
| ! [X: $i] :
( ~ ( product @ X @ Y @ R )
| ( product @ ( s @ X ) @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(26,plain,
( ( factorial @ n0 @ ( s @ n0 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(27,plain,
( ( ! [X: $i,Z: $i] :
( ~ ( factorial @ X @ Z )
| ! [Y: $i] :
( ~ ( product @ ( s @ X ) @ Z @ Y )
| ( factorial @ ( s @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(29,plain,
! [SV1: $i] :
( ( ~ ( factorial @ ( s @ ( s @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(30,plain,
! [SV2: $i] :
( ( sum @ SV2 @ n0 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(31,plain,
! [SV3: $i] :
( ( ! [SY13: $i,SY14: $i] :
( ~ ( sum @ SV3 @ SY13 @ SY14 )
| ( sum @ SV3 @ ( s @ SY13 ) @ ( s @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(32,plain,
! [SV4: $i] :
( ( product @ ( s @ n0 ) @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(33,plain,
! [SV5: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ~ ( sum @ SV5 @ SY15 @ SY16 )
| ! [SY17: $i] :
( ~ ( product @ SY17 @ SY15 @ SV5 )
| ( product @ ( s @ SY17 ) @ SY15 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(34,plain,
! [SV6: $i] :
( ( ! [SY18: $i] :
( ~ ( factorial @ SV6 @ SY18 )
| ! [SY19: $i] :
( ~ ( product @ ( s @ SV6 ) @ SY18 @ SY19 )
| ( factorial @ ( s @ SV6 ) @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV1: $i] :
( ( factorial @ ( s @ ( s @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY20: $i] :
( ~ ( sum @ SV3 @ SV7 @ SY20 )
| ( sum @ SV3 @ ( s @ SV7 ) @ ( s @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV8: $i,SV5: $i] :
( ( ! [SY21: $i] :
( ~ ( sum @ SV5 @ SV8 @ SY21 )
| ! [SY22: $i] :
( ~ ( product @ SY22 @ SV8 @ SV5 )
| ( product @ ( s @ SY22 ) @ SV8 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV9: $i,SV6: $i] :
( ( ~ ( factorial @ SV6 @ SV9 )
| ! [SY23: $i] :
( ~ ( product @ ( s @ SV6 ) @ SV9 @ SY23 )
| ( factorial @ ( s @ SV6 ) @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ~ ( sum @ SV3 @ SV7 @ SV10 )
| ( sum @ SV3 @ ( s @ SV7 ) @ ( s @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ~ ( sum @ SV5 @ SV8 @ SV11 )
| ! [SY24: $i] :
( ~ ( product @ SY24 @ SV8 @ SV5 )
| ( product @ ( s @ SY24 ) @ SV8 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV9: $i,SV6: $i] :
( ( ( ~ ( factorial @ SV6 @ SV9 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( product @ ( s @ SV6 ) @ SV9 @ SY23 )
| ( factorial @ ( s @ SV6 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( sum @ SV3 @ SV7 @ SV10 ) )
= $true )
| ( ( sum @ SV3 @ ( s @ SV7 ) @ ( s @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( sum @ SV5 @ SV8 @ SV11 ) )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( product @ SY24 @ SV8 @ SV5 )
| ( product @ ( s @ SY24 ) @ SV8 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV9: $i,SV6: $i] :
( ( ( factorial @ SV6 @ SV9 )
= $false )
| ( ( ! [SY23: $i] :
( ~ ( product @ ( s @ SV6 ) @ SV9 @ SY23 )
| ( factorial @ ( s @ SV6 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( sum @ SV3 @ SV7 @ SV10 )
= $false )
| ( ( sum @ SV3 @ ( s @ SV7 ) @ ( s @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV11: $i,SV8: $i,SV5: $i] :
( ( ( sum @ SV5 @ SV8 @ SV11 )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( product @ SY24 @ SV8 @ SV5 )
| ( product @ ( s @ SY24 ) @ SV8 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( product @ ( s @ SV6 ) @ SV9 @ SV12 )
| ( factorial @ ( s @ SV6 ) @ SV12 ) )
= $true )
| ( ( factorial @ SV6 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV11: $i,SV5: $i,SV8: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV8 @ SV5 )
| ( product @ ( s @ SV13 ) @ SV8 @ SV11 ) )
= $true )
| ( ( sum @ SV5 @ SV8 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ( ~ ( product @ ( s @ SV6 ) @ SV9 @ SV12 ) )
= $true )
| ( ( factorial @ ( s @ SV6 ) @ SV12 )
= $true )
| ( ( factorial @ SV6 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV11: $i,SV5: $i,SV8: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV8 @ SV5 ) )
= $true )
| ( ( product @ ( s @ SV13 ) @ SV8 @ SV11 )
= $true )
| ( ( sum @ SV5 @ SV8 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV12: $i,SV9: $i,SV6: $i] :
( ( ( product @ ( s @ SV6 ) @ SV9 @ SV12 )
= $false )
| ( ( factorial @ ( s @ SV6 ) @ SV12 )
= $true )
| ( ( factorial @ SV6 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV11: $i,SV5: $i,SV8: $i,SV13: $i] :
( ( ( product @ SV13 @ SV8 @ SV5 )
= $false )
| ( ( product @ ( s @ SV13 ) @ SV8 @ SV11 )
= $true )
| ( ( sum @ SV5 @ SV8 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(54,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,53,52,46,36,35,32,30]) ).
thf(55,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM283-1.005 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n004.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 : Thu Jul 7 01:05:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 7
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:7,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:9,loop_count:0,foatp_calls:0,translation:fof_full)..
% 9.55/9.73
% 9.55/9.73 ********************************
% 9.55/9.73 * All subproblems solved! *
% 9.55/9.73 ********************************
% 9.55/9.73 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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)
% 9.55/9.73
% 9.55/9.73 %**** Beginning of derivation protocol ****
% 9.55/9.73 % SZS output start CNFRefutation
% See solution above
% 9.55/9.73
% 9.55/9.73 %**** End of derivation protocol ****
% 9.55/9.73 %**** no. of clauses in derivation: 55 ****
% 9.55/9.73 %**** clause counter: 54 ****
% 9.55/9.73
% 9.55/9.73 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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)
%------------------------------------------------------------------------------