TSTP Solution File: BOO034-1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : BOO034-1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Thu Jul 14 23:43:37 EDT 2022
% Result : Unsatisfiable 0.17s 0.52s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 50 ( 41 unt; 9 typ; 0 def)
% Number of atoms : 107 ( 66 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 311 ( 6 ~; 0 |; 0 &; 305 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-3 aty)
% Number of variables : 80 ( 0 ^ 80 !; 0 ?; 80 :)
% 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_e,type,
e: $i ).
thf(tp_f,type,
f: $i ).
thf(tp_g,type,
g: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ Y @ ( inverse @ Y ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(2,axiom,
! [Y: $i,X: $i] :
( ( multiply @ ( inverse @ Y ) @ Y @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ X @ Y )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_2) ).
thf(4,axiom,
! [Y: $i,X: $i] :
( ( multiply @ Y @ X @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_1) ).
thf(5,axiom,
! [V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ V @ W @ X ) @ Y @ ( multiply @ V @ W @ Z ) )
= ( multiply @ V @ W @ ( multiply @ X @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
( multiply @ ( multiply @ a @ ( inverse @ a ) @ b ) @ ( inverse @ ( multiply @ ( multiply @ c @ d @ e ) @ f @ ( multiply @ c @ d @ g ) ) ) @ ( multiply @ d @ ( multiply @ g @ f @ e ) @ c ) )
!= b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_single_axiom) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y @ ( inverse @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ ( inverse @ Y ) @ Y @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ X @ Y )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ Y @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ V @ W @ X ) @ Y @ ( multiply @ V @ W @ Z ) )
= ( multiply @ V @ W @ ( multiply @ X @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ( ( multiply @ ( multiply @ a @ ( inverse @ a ) @ b ) @ ( inverse @ ( multiply @ ( multiply @ c @ d @ e ) @ f @ ( multiply @ c @ d @ g ) ) ) @ ( multiply @ d @ ( multiply @ g @ f @ e ) @ c ) )
!= b ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ( ( multiply @ ( multiply @ a @ ( inverse @ a ) @ b ) @ ( inverse @ ( multiply @ ( multiply @ c @ d @ e ) @ f @ ( multiply @ c @ d @ g ) ) ) @ ( multiply @ d @ ( multiply @ g @ f @ e ) @ c ) )
!= b ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(18,plain,
( ( ( ( multiply @ ( multiply @ a @ ( inverse @ a ) @ b ) @ ( inverse @ ( multiply @ ( multiply @ c @ d @ e ) @ f @ ( multiply @ c @ d @ g ) ) ) @ ( multiply @ d @ ( multiply @ g @ f @ e ) @ c ) )
!= b ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ V @ W @ X ) @ Y @ ( multiply @ V @ W @ Z ) )
= ( multiply @ V @ W @ ( multiply @ X @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ Y @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ X @ Y )
= X ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ ( inverse @ Y ) @ Y @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y @ ( inverse @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ( multiply @ ( multiply @ a @ ( inverse @ a ) @ b ) @ ( inverse @ ( multiply @ ( multiply @ c @ d @ e ) @ f @ ( multiply @ c @ d @ g ) ) ) @ ( multiply @ d @ ( multiply @ g @ f @ e ) @ c ) )
= b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV1: $i] :
( ( ! [SY13: $i,SY14: $i,SY15: $i,SY16: $i] :
( ( multiply @ ( multiply @ SV1 @ SY13 @ SY14 ) @ SY15 @ ( multiply @ SV1 @ SY13 @ SY16 ) )
= ( multiply @ SV1 @ SY13 @ ( multiply @ SY14 @ SY15 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV2: $i] :
( ( ! [SY17: $i] :
( ( multiply @ SV2 @ SY17 @ SY17 )
= SY17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV3: $i] :
( ( ! [SY18: $i] :
( ( multiply @ SV3 @ SV3 @ SY18 )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV4: $i] :
( ( ! [SY19: $i] :
( ( multiply @ ( inverse @ SV4 ) @ SV4 @ SY19 )
= SY19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV5: $i] :
( ( ! [SY20: $i] :
( ( multiply @ SV5 @ SY20 @ ( inverse @ SY20 ) )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY21: $i,SY22: $i,SY23: $i] :
( ( multiply @ ( multiply @ SV1 @ SV6 @ SY21 ) @ SY22 @ ( multiply @ SV1 @ SV6 @ SY23 ) )
= ( multiply @ SV1 @ SV6 @ ( multiply @ SY21 @ SY22 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV7: $i,SV2: $i] :
( ( ( multiply @ SV2 @ SV7 @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV8: $i,SV3: $i] :
( ( ( multiply @ SV3 @ SV3 @ SV8 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV9: $i,SV4: $i] :
( ( ( multiply @ ( inverse @ SV4 ) @ SV4 @ SV9 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV10: $i,SV5: $i] :
( ( ( multiply @ SV5 @ SV10 @ ( inverse @ SV10 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ( multiply @ ( multiply @ SV1 @ SV6 @ SV11 ) @ SY24 @ ( multiply @ SV1 @ SV6 @ SY25 ) )
= ( multiply @ SV1 @ SV6 @ ( multiply @ SV11 @ SY24 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV12: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ! [SY26: $i] :
( ( multiply @ ( multiply @ SV1 @ SV6 @ SV11 ) @ SV12 @ ( multiply @ SV1 @ SV6 @ SY26 ) )
= ( multiply @ SV1 @ SV6 @ ( multiply @ SV11 @ SV12 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV13: $i,SV12: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ( multiply @ ( multiply @ SV1 @ SV6 @ SV11 ) @ SV12 @ ( multiply @ SV1 @ SV6 @ SV13 ) )
= ( multiply @ SV1 @ SV6 @ ( multiply @ SV11 @ SV12 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,39,36,35,34,33,31]) ).
thf(41,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO034-1 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Wed Jun 1 18:44:44 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.11/0.32
% 0.11/0.32 No.of.Axioms: 6
% 0.11/0.32
% 0.11/0.32 Length.of.Defs: 0
% 0.11/0.32
% 0.11/0.32 Contains.Choice.Funs: false
% 0.11/0.33 (rf:0,axioms:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.17/0.52
% 0.17/0.52 ********************************
% 0.17/0.52 * All subproblems solved! *
% 0.17/0.52 ********************************
% 0.17/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:40,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.17/0.52
% 0.17/0.52 %**** Beginning of derivation protocol ****
% 0.17/0.52 % SZS output start CNFRefutation
% See solution above
% 0.17/0.52
% 0.17/0.52 %**** End of derivation protocol ****
% 0.17/0.52 %**** no. of clauses in derivation: 41 ****
% 0.17/0.52 %**** clause counter: 40 ****
% 0.17/0.52
% 0.17/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:40,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------