TSTP Solution File: GRP002-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.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 10:15:18 EDT 2022
% Result : Unsatisfiable 0.39s 0.59s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 23
% Syntax : Number of formulae : 64 ( 54 unt; 10 typ; 0 def)
% Number of atoms : 134 ( 86 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 164 ( 6 ~; 0 |; 0 &; 158 @)
% ( 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 : 13 ( 10 usr; 10 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_d,type,
d: $i ).
thf(tp_h,type,
h: $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_j,type,
j: $i ).
thf(tp_k,type,
k: $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,
! [X: $i] :
( ( multiply @ X @ ( multiply @ X @ X ) )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity) ).
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,
( multiply @ k @ ( inverse @ b ) )
!= identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
thf(10,negated_conjecture,
( ( multiply @ j @ ( inverse @ h ) )
= k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
thf(11,negated_conjecture,
( ( multiply @ h @ b )
= j ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_b_is_j) ).
thf(12,negated_conjecture,
( ( multiply @ d @ ( inverse @ b ) )
= h ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
thf(13,negated_conjecture,
( ( multiply @ c @ ( inverse @ a ) )
= d ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
thf(14,negated_conjecture,
( ( multiply @ a @ b )
= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
thf(15,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [X: $i] :
( ( multiply @ X @ identity )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,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(19,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( multiply @ X @ X ) )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ( ( multiply @ k @ ( inverse @ b ) )
!= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ( multiply @ j @ ( inverse @ h ) )
= k )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(24,plain,
( ( ( multiply @ h @ b )
= j )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(25,plain,
( ( ( multiply @ d @ ( inverse @ b ) )
= h )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(26,plain,
( ( ( multiply @ c @ ( inverse @ a ) )
= d )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(27,plain,
( ( ( multiply @ a @ b )
= c )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,plain,
( ( ( ( multiply @ k @ ( inverse @ b ) )
!= identity ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(30,plain,
( ( ( multiply @ a @ b )
= c )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(31,plain,
( ( ( multiply @ c @ ( inverse @ a ) )
= d )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(32,plain,
( ( ( multiply @ d @ ( inverse @ b ) )
= h )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(33,plain,
( ( ( multiply @ h @ b )
= j )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(34,plain,
( ( ( multiply @ j @ ( inverse @ h ) )
= k )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(35,plain,
( ( ( ( multiply @ k @ ( inverse @ b ) )
!= identity ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(36,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( multiply @ X @ X ) )
= identity ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(38,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(40,plain,
( ( ! [X: $i] :
( ( multiply @ X @ identity )
= X ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(41,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= identity ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(42,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,plain,
( ( ( multiply @ k @ ( inverse @ b ) )
= identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV1: $i] :
( ( ( multiply @ SV1 @ ( multiply @ SV1 @ SV1 ) )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV2: $i] :
( ( ( multiply @ identity @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV3: $i] :
( ( ( multiply @ ( inverse @ SV3 ) @ SV3 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV4: $i] :
( ( ! [SY8: $i,SY9: $i] :
( ( multiply @ ( multiply @ SV4 @ SY8 ) @ SY9 )
= ( multiply @ SV4 @ ( multiply @ SY8 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV5: $i] :
( ( ( multiply @ SV5 @ identity )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV6: $i] :
( ( ( multiply @ SV6 @ ( inverse @ SV6 ) )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV7: $i,SV4: $i] :
( ( ! [SY10: $i] :
( ( multiply @ ( multiply @ SV4 @ SV7 ) @ SY10 )
= ( multiply @ SV4 @ ( multiply @ SV7 @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV8: $i,SV7: $i,SV4: $i] :
( ( ( multiply @ ( multiply @ SV4 @ SV7 ) @ SV8 )
= ( multiply @ SV4 @ ( multiply @ SV7 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(53,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,52,50,49,48,46,45,44,43,34,33,32,31]) ).
thf(54,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 06:19:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 12
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:12,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:14,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.39/0.59
% 0.39/0.59 ********************************
% 0.39/0.59 * All subproblems solved! *
% 0.39/0.59 ********************************
% 0.39/0.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:53,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.39/0.59
% 0.39/0.59 %**** Beginning of derivation protocol ****
% 0.39/0.59 % SZS output start CNFRefutation
% See solution above
% 0.39/0.59
% 0.39/0.59 %**** End of derivation protocol ****
% 0.39/0.59 %**** no. of clauses in derivation: 54 ****
% 0.39/0.59 %**** clause counter: 53 ****
% 0.39/0.59
% 0.39/0.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:53,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------