TSTP Solution File: GRP068-1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP068-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.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 10:15:45 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 45 ( 30 unt; 9 typ; 0 def)
% Number of atoms : 128 ( 83 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 291 ( 22 ~; 18 |; 0 &; 251 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 36 ( 0 ^ 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a1,type,
a1: $i ).
thf(tp_a2,type,
a2: $i ).
thf(tp_a3,type,
a3: $i ).
thf(tp_b3,type,
b3: $i ).
thf(tp_c3,type,
c3: $i ).
thf(tp_divide,type,
divide: $i > $i > $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [X: $i] :
( identity
= ( divide @ X @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
thf(2,axiom,
! [X: $i] :
( ( inverse @ X )
= ( divide @ identity @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( divide @ X @ ( divide @ identity @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( divide @ X @ ( divide @ ( divide @ ( divide @ identity @ Y ) @ Z ) @ ( divide @ ( divide @ ( divide @ X @ X ) @ X ) @ Z ) ) )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
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,
( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity )
| ( ( multiply @ identity @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [X: $i] :
( identity
= ( divide @ X @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [X: $i] :
( ( inverse @ X )
= ( divide @ identity @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( divide @ X @ ( divide @ identity @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( divide @ X @ ( divide @ ( divide @ ( divide @ identity @ Y ) @ Z ) @ ( divide @ ( divide @ ( divide @ X @ X ) @ X ) @ Z ) ) )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity )
| ( ( multiply @ identity @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity )
| ( ( multiply @ identity @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(16,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity )
| ( ( multiply @ identity @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( divide @ X @ ( divide @ ( divide @ ( divide @ identity @ Y ) @ Z ) @ ( divide @ ( divide @ ( divide @ X @ X ) @ X ) @ Z ) ) )
= Y ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( divide @ X @ ( divide @ identity @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [X: $i] :
( ( inverse @ X )
= ( divide @ identity @ X ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [X: $i] :
( identity
= ( divide @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(21,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(22,plain,
( ( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity ) )
= $true )
| ( ( ( ( multiply @ identity @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV1: $i] :
( ( ! [SY7: $i,SY8: $i] :
( ( divide @ SV1 @ ( divide @ ( divide @ ( divide @ identity @ SY7 ) @ SY8 ) @ ( divide @ ( divide @ ( divide @ SV1 @ SV1 ) @ SV1 ) @ SY8 ) ) )
= SY7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV2: $i] :
( ( ! [SY9: $i] :
( ( multiply @ SV2 @ SY9 )
= ( divide @ SV2 @ ( divide @ identity @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV3: $i] :
( ( ( inverse @ SV3 )
= ( divide @ identity @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV4: $i] :
( ( identity
= ( divide @ SV4 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(28,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= identity )
= $false )
| ( ( ( ( multiply @ identity @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY10: $i] :
( ( divide @ SV1 @ ( divide @ ( divide @ ( divide @ identity @ SV5 ) @ SY10 ) @ ( divide @ ( divide @ ( divide @ SV1 @ SV1 ) @ SV1 ) @ SY10 ) ) )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV6: $i,SV2: $i] :
( ( ( multiply @ SV2 @ SV6 )
= ( divide @ SV2 @ ( divide @ identity @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
( ( ( ( ( multiply @ identity @ a2 )
!= a2 ) )
= $true )
| ( ( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) )
= $true )
| ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= identity )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV7: $i,SV5: $i,SV1: $i] :
( ( ( divide @ SV1 @ ( divide @ ( divide @ ( divide @ identity @ SV5 ) @ SV7 ) @ ( divide @ ( divide @ ( divide @ SV1 @ SV1 ) @ SV1 ) @ SV7 ) ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ( ( multiply @ identity @ a2 )
= a2 )
= $false )
| ( ( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) )
= $true )
| ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= identity )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
( ( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
= $false )
| ( ( ( multiply @ identity @ a2 )
= a2 )
= $false )
| ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= identity )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,34,32,30,27,26]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP068-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n018.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 Jun 14 10:49:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 5
% 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: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).
% 0.19/0.42
% 0.19/0.42 ********************************
% 0.19/0.42 * All subproblems solved! *
% 0.19/0.42 ********************************
% 0.19/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/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:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.42
% 0.19/0.42 %**** Beginning of derivation protocol ****
% 0.19/0.42 % SZS output start CNFRefutation
% See solution above
% 0.19/0.42
% 0.19/0.42 %**** End of derivation protocol ****
% 0.19/0.42 %**** no. of clauses in derivation: 36 ****
% 0.19/0.42 %**** clause counter: 35 ****
% 0.19/0.42
% 0.19/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/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:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------