TSTP Solution File: GRP001-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP001-2 : 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 : n025.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 10:15:16 EDT 2022
% Result : Unsatisfiable 0.19s 0.38s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 48 ( 42 unt; 6 typ; 0 def)
% Number of atoms : 106 ( 66 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 118 ( 6 ~; 0 |; 0 &; 112 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 38 ( 0 ^ 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $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] :
( ( multiply @ X @ ( inverse @ X ) )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(2,axiom,
! [X: $i] :
( ( multiply @ X @ identity )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(4,axiom,
! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(5,axiom,
! [X: $i] :
( ( multiply @ identity @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(6,axiom,
( ( multiply @ a @ b )
= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
thf(7,axiom,
! [X: $i] :
( ( multiply @ X @ X )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',squareness) ).
thf(8,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(9,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,negated_conjecture,
( multiply @ b @ a )
!= c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
thf(11,plain,
$false = $false,
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [X: $i] :
( ( multiply @ X @ identity )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ( multiply @ a @ b )
= c )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [X: $i] :
( ( multiply @ X @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ( ( multiply @ b @ a )
!= c ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( ( ( multiply @ b @ a )
!= c ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(22,plain,
( ( ( ( multiply @ b @ a )
!= c ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [X: $i] :
( ( multiply @ X @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(24,plain,
( ( ( multiply @ a @ b )
= c )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(26,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( multiply @ X @ identity )
= X ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= identity ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(31,plain,
( ( ( multiply @ b @ a )
= c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(32,plain,
! [SV1: $i] :
( ( ( multiply @ SV1 @ SV1 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(33,plain,
! [SV2: $i] :
( ( ( multiply @ identity @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(34,plain,
! [SV3: $i] :
( ( ( multiply @ ( inverse @ SV3 ) @ SV3 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV4: $i] :
( ( ! [SY8: $i,SY9: $i] :
( ( multiply @ ( multiply @ SV4 @ SY8 ) @ SY9 )
= ( multiply @ SV4 @ ( multiply @ SY8 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
! [SV5: $i] :
( ( ( multiply @ SV5 @ identity )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV6: $i] :
( ( ( multiply @ SV6 @ ( inverse @ SV6 ) )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(39,plain,
! [SV7: $i,SV4: $i] :
( ( ! [SY10: $i] :
( ( multiply @ ( multiply @ SV4 @ SV7 ) @ SY10 )
= ( multiply @ SV4 @ ( multiply @ SV7 @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV8: $i,SV7: $i,SV4: $i] :
( ( ( multiply @ ( multiply @ SV4 @ SV7 ) @ SV8 )
= ( multiply @ SV4 @ ( multiply @ SV7 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,40,38,37,36,34,33,32,31]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP001-2 : 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 : n025.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
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 18:43:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 8
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:8,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:10,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.19/0.38
% 0.19/0.38 ********************************
% 0.19/0.38 * All subproblems solved! *
% 0.19/0.38 ********************************
% 0.19/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.38
% 0.19/0.38 %**** Beginning of derivation protocol ****
% 0.19/0.38 % SZS output start CNFRefutation
% See solution above
% 0.19/0.38
% 0.19/0.38 %**** End of derivation protocol ****
% 0.19/0.38 %**** no. of clauses in derivation: 42 ****
% 0.19/0.38 %**** clause counter: 41 ****
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------