TSTP Solution File: GRP028-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP028-1 : 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 : n032.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 : Sat Jul 16 10:15:30 EDT 2022
% Result : Unsatisfiable 0.14s 0.33s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 30 unt; 4 typ; 0 def)
% Number of atoms : 183 ( 48 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 357 ( 42 ~; 48 |; 0 &; 267 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 121 ( 0 ^ 121 !; 0 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_left_solution,type,
left_solution: $i > $i > $i ).
thf(tp_not_identity,type,
not_identity: $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(tp_right_solution,type,
right_solution: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(2,axiom,
! [X: $i,Y: $i] : ( product @ X @ ( right_solution @ X @ Y ) @ Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_soln) ).
thf(3,axiom,
! [X: $i,Y: $i] : ( product @ ( left_solution @ X @ Y ) @ X @ Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_soln) ).
thf(4,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(5,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,negated_conjecture,
! [X: $i] :
~ ( product @ ( not_identity @ X ) @ X @ ( not_identity @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
thf(7,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ ( right_solution @ X @ Y ) @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] : ( product @ ( left_solution @ X @ Y ) @ X @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [X: $i] :
~ ( product @ ( not_identity @ X ) @ X @ ( not_identity @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( ! [X: $i] :
~ ( product @ ( not_identity @ X ) @ X @ ( not_identity @ X ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] : ( product @ ( left_solution @ X @ Y ) @ X @ Y ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ ( right_solution @ X @ Y ) @ Y ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(18,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
! [SV1: $i] :
( ( ~ ( product @ ( not_identity @ SV1 ) @ SV1 @ ( not_identity @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(20,plain,
! [SV2: $i] :
( ( ! [SY11: $i] : ( product @ ( left_solution @ SV2 @ SY11 ) @ SV2 @ SY11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV3: $i] :
( ( ! [SY12: $i] : ( product @ SV3 @ ( right_solution @ SV3 @ SY12 ) @ SY12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV4: $i] :
( ( ! [SY13: $i,SY14: $i,SY15: $i] :
( ~ ( product @ SV4 @ SY13 @ SY14 )
| ! [SY16: $i] :
( ~ ( product @ SY13 @ SY15 @ SY16 )
| ! [SY17: $i] :
( ~ ( product @ SV4 @ SY16 @ SY17 )
| ( product @ SY14 @ SY15 @ SY17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV1: $i] :
( ( product @ ( not_identity @ SV1 ) @ SV1 @ ( not_identity @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV5: $i,SV2: $i] :
( ( product @ ( left_solution @ SV2 @ SV5 ) @ SV2 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV6: $i,SV3: $i] :
( ( product @ SV3 @ ( right_solution @ SV3 @ SV6 ) @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV7: $i,SV4: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( product @ SV4 @ SV7 @ SY18 )
| ! [SY20: $i] :
( ~ ( product @ SV7 @ SY19 @ SY20 )
| ! [SY17: $i] :
( ~ ( product @ SV4 @ SY20 @ SY17 )
| ( product @ SY18 @ SY19 @ SY17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV8: $i,SV7: $i,SV4: $i] :
( ( ! [SY22: $i] :
( ~ ( product @ SV4 @ SV7 @ SV8 )
| ! [SY23: $i] :
( ~ ( product @ SV7 @ SY22 @ SY23 )
| ! [SY24: $i] :
( ~ ( product @ SV4 @ SY23 @ SY24 )
| ( product @ SV8 @ SY22 @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(29,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV4: $i] :
( ( ~ ( product @ SV4 @ SV7 @ SV8 )
| ! [SY25: $i] :
( ~ ( product @ SV7 @ SV9 @ SY25 )
| ! [SY26: $i] :
( ~ ( product @ SV4 @ SY25 @ SY26 )
| ( product @ SV8 @ SV9 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(30,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( product @ SV4 @ SV7 @ SV8 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( product @ SV7 @ SV9 @ SY25 )
| ! [SY26: $i] :
( ~ ( product @ SV4 @ SY25 @ SY26 )
| ( product @ SV8 @ SV9 @ SY26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(31,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV4: $i] :
( ( ( product @ SV4 @ SV7 @ SV8 )
= $false )
| ( ( ! [SY25: $i] :
( ~ ( product @ SV7 @ SV9 @ SY25 )
| ! [SY26: $i] :
( ~ ( product @ SV4 @ SY25 @ SY26 )
| ( product @ SV8 @ SV9 @ SY26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(32,plain,
! [SV8: $i,SV4: $i,SV10: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV9 @ SV10 )
| ! [SY27: $i] :
( ~ ( product @ SV4 @ SV10 @ SY27 )
| ( product @ SV8 @ SV9 @ SY27 ) ) )
= $true )
| ( ( product @ SV4 @ SV7 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(33,plain,
! [SV8: $i,SV4: $i,SV10: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV9 @ SV10 ) )
= $true )
| ( ( ! [SY27: $i] :
( ~ ( product @ SV4 @ SV10 @ SY27 )
| ( product @ SV8 @ SV9 @ SY27 ) ) )
= $true )
| ( ( product @ SV4 @ SV7 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(34,plain,
! [SV8: $i,SV4: $i,SV10: $i,SV9: $i,SV7: $i] :
( ( ( product @ SV7 @ SV9 @ SV10 )
= $false )
| ( ( ! [SY27: $i] :
( ~ ( product @ SV4 @ SV10 @ SY27 )
| ( product @ SV8 @ SV9 @ SY27 ) ) )
= $true )
| ( ( product @ SV4 @ SV7 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(35,plain,
! [SV7: $i,SV9: $i,SV8: $i,SV11: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( product @ SV4 @ SV10 @ SV11 )
| ( product @ SV8 @ SV9 @ SV11 ) )
= $true )
| ( ( product @ SV7 @ SV9 @ SV10 )
= $false )
| ( ( product @ SV4 @ SV7 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(36,plain,
! [SV7: $i,SV9: $i,SV8: $i,SV11: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( product @ SV4 @ SV10 @ SV11 ) )
= $true )
| ( ( product @ SV8 @ SV9 @ SV11 )
= $true )
| ( ( product @ SV7 @ SV9 @ SV10 )
= $false )
| ( ( product @ SV4 @ SV7 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(37,plain,
! [SV7: $i,SV9: $i,SV8: $i,SV11: $i,SV10: $i,SV4: $i] :
( ( ( product @ SV4 @ SV10 @ SV11 )
= $false )
| ( ( product @ SV8 @ SV9 @ SV11 )
= $true )
| ( ( product @ SV7 @ SV9 @ SV10 )
= $false )
| ( ( product @ SV4 @ SV7 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(38,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,37,26,25,24]) ).
thf(39,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP028-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.11 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Tue Jun 14 11:50:42 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.10/0.30
% 0.10/0.30 No.of.Axioms: 4
% 0.10/0.30
% 0.10/0.30 Length.of.Defs: 0
% 0.10/0.30
% 0.10/0.30 Contains.Choice.Funs: false
% 0.10/0.30 (rf:0,axioms:4,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:6,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.14/0.33
% 0.14/0.33 ********************************
% 0.14/0.33 * All subproblems solved! *
% 0.14/0.33 ********************************
% 0.14/0.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:38,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.33
% 0.14/0.33 %**** Beginning of derivation protocol ****
% 0.14/0.33 % SZS output start CNFRefutation
% See solution above
% 0.14/0.33
% 0.14/0.33 %**** End of derivation protocol ****
% 0.14/0.33 %**** no. of clauses in derivation: 39 ****
% 0.14/0.33 %**** clause counter: 38 ****
% 0.14/0.33
% 0.14/0.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:38,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------