TSTP Solution File: GRP004-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP004-1 : 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 : n014.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 10:15:20 EDT 2022
% Result : Unsatisfiable 0.21s 0.41s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 35 unt; 4 typ; 0 def)
% Number of atoms : 301 ( 76 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 601 ( 78 ~; 96 |; 0 &; 427 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-3 aty)
% Number of variables : 205 ( 0 ^ 205 !; 0 ?; 205 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
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/sandbox/benchmark/theBenchmark.p',associativity2) ).
thf(2,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
thf(3,axiom,
! [X: $i] : ( product @ identity @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(4,axiom,
! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
! [X: $i] :
~ ( product @ a @ X @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_right_inverse) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(9,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(10,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [X: $i] :
~ ( product @ a @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,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)],[9]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(17,plain,
( ( ! [X: $i] :
~ ( product @ a @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(18,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(21,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)],[15]) ).
thf(22,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(23,plain,
! [SV1: $i] :
( ( ~ ( product @ a @ SV1 @ identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV2: $i] :
( ( product @ ( inverse @ SV2 ) @ SV2 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV3: $i] :
( ( product @ identity @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV4: $i] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ~ ( product @ SV4 @ SY15 @ SY16 )
| ! [SY18: $i] :
( ~ ( product @ SY15 @ SY17 @ SY18 )
| ! [SY19: $i] :
( ~ ( product @ SY16 @ SY17 @ SY19 )
| ( product @ SV4 @ SY18 @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV5: $i] :
( ( ! [SY20: $i,SY21: $i,SY22: $i] :
( ~ ( product @ SV5 @ SY20 @ SY21 )
| ! [SY23: $i] :
( ~ ( product @ SY20 @ SY22 @ SY23 )
| ! [SY24: $i] :
( ~ ( product @ SV5 @ SY23 @ SY24 )
| ( product @ SY21 @ SY22 @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV1: $i] :
( ( product @ a @ SV1 @ identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV6: $i,SV4: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( product @ SV4 @ SV6 @ SY25 )
| ! [SY27: $i] :
( ~ ( product @ SV6 @ SY26 @ SY27 )
| ! [SY19: $i] :
( ~ ( product @ SY25 @ SY26 @ SY19 )
| ( product @ SV4 @ SY27 @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV7: $i,SV5: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( product @ SV5 @ SV7 @ SY29 )
| ! [SY31: $i] :
( ~ ( product @ SV7 @ SY30 @ SY31 )
| ! [SY24: $i] :
( ~ ( product @ SV5 @ SY31 @ SY24 )
| ( product @ SY29 @ SY30 @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV8: $i,SV6: $i,SV4: $i] :
( ( ! [SY33: $i] :
( ~ ( product @ SV4 @ SV6 @ SV8 )
| ! [SY34: $i] :
( ~ ( product @ SV6 @ SY33 @ SY34 )
| ! [SY35: $i] :
( ~ ( product @ SV8 @ SY33 @ SY35 )
| ( product @ SV4 @ SY34 @ SY35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ! [SY36: $i] :
( ~ ( product @ SV5 @ SV7 @ SV9 )
| ! [SY37: $i] :
( ~ ( product @ SV7 @ SY36 @ SY37 )
| ! [SY38: $i] :
( ~ ( product @ SV5 @ SY37 @ SY38 )
| ( product @ SV9 @ SY36 @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ~ ( product @ SV4 @ SV6 @ SV8 )
| ! [SY39: $i] :
( ~ ( product @ SV6 @ SV10 @ SY39 )
| ! [SY40: $i] :
( ~ ( product @ SV8 @ SV10 @ SY40 )
| ( product @ SV4 @ SY39 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV5: $i] :
( ( ~ ( product @ SV5 @ SV7 @ SV9 )
| ! [SY41: $i] :
( ~ ( product @ SV7 @ SV11 @ SY41 )
| ! [SY42: $i] :
( ~ ( product @ SV5 @ SY41 @ SY42 )
| ( product @ SV9 @ SV11 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ( ~ ( product @ SV4 @ SV6 @ SV8 ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( product @ SV6 @ SV10 @ SY39 )
| ! [SY40: $i] :
( ~ ( product @ SV8 @ SV10 @ SY40 )
| ( product @ SV4 @ SY39 @ SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV7 @ SV9 ) )
= $true )
| ( ( ! [SY41: $i] :
( ~ ( product @ SV7 @ SV11 @ SY41 )
| ! [SY42: $i] :
( ~ ( product @ SV5 @ SY41 @ SY42 )
| ( product @ SV9 @ SV11 @ SY42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ( product @ SV4 @ SV6 @ SV8 )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( product @ SV6 @ SV10 @ SY39 )
| ! [SY40: $i] :
( ~ ( product @ SV8 @ SV10 @ SY40 )
| ( product @ SV4 @ SY39 @ SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV5: $i] :
( ( ( product @ SV5 @ SV7 @ SV9 )
= $false )
| ( ( ! [SY41: $i] :
( ~ ( product @ SV7 @ SV11 @ SY41 )
| ! [SY42: $i] :
( ~ ( product @ SV5 @ SY41 @ SY42 )
| ( product @ SV9 @ SV11 @ SY42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV4: $i,SV8: $i,SV12: $i,SV10: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV10 @ SV12 )
| ! [SY43: $i] :
( ~ ( product @ SV8 @ SV10 @ SY43 )
| ( product @ SV4 @ SV12 @ SY43 ) ) )
= $true )
| ( ( product @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV9: $i,SV5: $i,SV13: $i,SV11: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV11 @ SV13 )
| ! [SY44: $i] :
( ~ ( product @ SV5 @ SV13 @ SY44 )
| ( product @ SV9 @ SV11 @ SY44 ) ) )
= $true )
| ( ( product @ SV5 @ SV7 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV4: $i,SV8: $i,SV12: $i,SV10: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV10 @ SV12 ) )
= $true )
| ( ( ! [SY43: $i] :
( ~ ( product @ SV8 @ SV10 @ SY43 )
| ( product @ SV4 @ SV12 @ SY43 ) ) )
= $true )
| ( ( product @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV9: $i,SV5: $i,SV13: $i,SV11: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV11 @ SV13 ) )
= $true )
| ( ( ! [SY44: $i] :
( ~ ( product @ SV5 @ SV13 @ SY44 )
| ( product @ SV9 @ SV11 @ SY44 ) ) )
= $true )
| ( ( product @ SV5 @ SV7 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV4: $i,SV8: $i,SV12: $i,SV10: $i,SV6: $i] :
( ( ( product @ SV6 @ SV10 @ SV12 )
= $false )
| ( ( ! [SY43: $i] :
( ~ ( product @ SV8 @ SV10 @ SY43 )
| ( product @ SV4 @ SV12 @ SY43 ) ) )
= $true )
| ( ( product @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV9: $i,SV5: $i,SV13: $i,SV11: $i,SV7: $i] :
( ( ( product @ SV7 @ SV11 @ SV13 )
= $false )
| ( ( ! [SY44: $i] :
( ~ ( product @ SV5 @ SV13 @ SY44 )
| ( product @ SV9 @ SV11 @ SY44 ) ) )
= $true )
| ( ( product @ SV5 @ SV7 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV6: $i,SV12: $i,SV4: $i,SV14: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV10 @ SV14 )
| ( product @ SV4 @ SV12 @ SV14 ) )
= $true )
| ( ( product @ SV6 @ SV10 @ SV12 )
= $false )
| ( ( product @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV7: $i,SV11: $i,SV9: $i,SV15: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV13 @ SV15 )
| ( product @ SV9 @ SV11 @ SV15 ) )
= $true )
| ( ( product @ SV7 @ SV11 @ SV13 )
= $false )
| ( ( product @ SV5 @ SV7 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV6: $i,SV12: $i,SV4: $i,SV14: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV10 @ SV14 ) )
= $true )
| ( ( product @ SV4 @ SV12 @ SV14 )
= $true )
| ( ( product @ SV6 @ SV10 @ SV12 )
= $false )
| ( ( product @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV7: $i,SV11: $i,SV9: $i,SV15: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV13 @ SV15 ) )
= $true )
| ( ( product @ SV9 @ SV11 @ SV15 )
= $true )
| ( ( product @ SV7 @ SV11 @ SV13 )
= $false )
| ( ( product @ SV5 @ SV7 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV6: $i,SV12: $i,SV4: $i,SV14: $i,SV10: $i,SV8: $i] :
( ( ( product @ SV8 @ SV10 @ SV14 )
= $false )
| ( ( product @ SV4 @ SV12 @ SV14 )
= $true )
| ( ( product @ SV6 @ SV10 @ SV12 )
= $false )
| ( ( product @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV7: $i,SV11: $i,SV9: $i,SV15: $i,SV13: $i,SV5: $i] :
( ( ( product @ SV5 @ SV13 @ SV15 )
= $false )
| ( ( product @ SV9 @ SV11 @ SV15 )
= $true )
| ( ( product @ SV7 @ SV11 @ SV13 )
= $false )
| ( ( product @ SV5 @ SV7 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,51,50,29,28,25]) ).
thf(53,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 09:25:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 5
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.21/0.41
% 0.21/0.41 ********************************
% 0.21/0.41 * All subproblems solved! *
% 0.21/0.41 ********************************
% 0.21/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:52,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.41
% 0.21/0.41 %**** Beginning of derivation protocol ****
% 0.21/0.41 % SZS output start CNFRefutation
% See solution above
% 0.21/0.41
% 0.21/0.41 %**** End of derivation protocol ****
% 0.21/0.41 %**** no. of clauses in derivation: 53 ****
% 0.21/0.41 %**** clause counter: 52 ****
% 0.21/0.41
% 0.21/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:52,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------