TSTP Solution File: LCL146-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL146-1 : 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 : n020.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 : Sun Jul 17 12:20:58 EDT 2022
% Result : Unsatisfiable 0.38s 0.57s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 66 ( 52 unt; 8 typ; 0 def)
% Number of atoms : 175 ( 101 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 342 ( 19 ~; 15 |; 0 &; 308 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 92 ( 0 ^ 92 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_V,type,
big_V: $i > $i > $i ).
thf(tp_big_hat,type,
big_hat: $i > $i > $i ).
thf(tp_implies,type,
implies: $i > $i > $i ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_ordered,type,
ordered: $i > $i > $o ).
thf(tp_truth,type,
truth: $i ).
thf(tp_x,type,
x: $i ).
thf(tp_y,type,
y: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( ( implies @ X @ Y )
!= truth )
| ( ordered @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition2) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ~ ( ordered @ X @ Y )
| ( ( implies @ X @ Y )
= truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition1) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( big_hat @ X @ Y )
= ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_hat_definition) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( big_V @ X @ Y )
= ( implies @ ( implies @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_V_definition) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( implies @ ( implies @ X @ Y ) @ Y )
= ( implies @ ( implies @ Y @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
thf(7,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
thf(8,axiom,
! [X: $i] :
( ( implies @ truth @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
( not @ ( big_hat @ x @ y ) )
!= ( big_V @ ( not @ x ) @ ( not @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i] :
( ( ( implies @ X @ Y )
!= truth )
| ( ordered @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( ordered @ X @ Y )
| ( ( implies @ X @ Y )
= truth ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] :
( ( big_hat @ X @ Y )
= ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] :
( ( big_V @ X @ Y )
= ( implies @ ( implies @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
= truth ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ( implies @ ( implies @ X @ Y ) @ Y )
= ( implies @ ( implies @ Y @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
= truth ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( implies @ truth @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ( ( not @ ( big_hat @ x @ y ) )
!= ( big_V @ ( not @ x ) @ ( not @ y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( ( implies @ X @ Y )
!= truth )
| ( ordered @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(24,plain,
( ( ( ( not @ ( big_hat @ x @ y ) )
!= ( big_V @ ( not @ x ) @ ( not @ y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(25,plain,
( ( ( ( not @ ( big_hat @ x @ y ) )
!= ( big_V @ ( not @ x ) @ ( not @ y ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(26,plain,
( ( ! [X: $i] :
( ( implies @ truth @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
= truth ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
( ( implies @ ( implies @ X @ Y ) @ Y )
= ( implies @ ( implies @ Y @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
= truth ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ( big_V @ X @ Y )
= ( implies @ ( implies @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( big_hat @ X @ Y )
= ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( ordered @ X @ Y )
| ( ( implies @ X @ Y )
= truth ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ( ( implies @ X @ Y )
!= truth )
| ( ordered @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( ( not @ ( big_hat @ x @ y ) )
= ( big_V @ ( not @ x ) @ ( not @ y ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV1: $i] :
( ( ( implies @ truth @ SV1 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV2: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ( implies @ ( implies @ SV2 @ SY16 ) @ ( implies @ ( implies @ SY16 @ SY17 ) @ ( implies @ SV2 @ SY17 ) ) )
= truth ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(38,plain,
! [SV3: $i] :
( ( ! [SY18: $i] :
( ( implies @ ( implies @ SV3 @ SY18 ) @ SY18 )
= ( implies @ ( implies @ SY18 @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(39,plain,
! [SV4: $i] :
( ( ! [SY19: $i] :
( ( implies @ ( implies @ ( not @ SV4 ) @ ( not @ SY19 ) ) @ ( implies @ SY19 @ SV4 ) )
= truth ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(40,plain,
! [SV5: $i] :
( ( ! [SY20: $i] :
( ( big_V @ SV5 @ SY20 )
= ( implies @ ( implies @ SV5 @ SY20 ) @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV6: $i] :
( ( ! [SY21: $i] :
( ( big_hat @ SV6 @ SY21 )
= ( not @ ( big_V @ ( not @ SV6 ) @ ( not @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
! [SV7: $i] :
( ( ! [SY22: $i] :
( ~ ( ordered @ SV7 @ SY22 )
| ( ( implies @ SV7 @ SY22 )
= truth ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(43,plain,
! [SV8: $i] :
( ( ! [SY23: $i] :
( ( ( implies @ SV8 @ SY23 )
!= truth )
| ( ordered @ SV8 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(44,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(45,plain,
! [SV9: $i,SV2: $i] :
( ( ! [SY24: $i] :
( ( implies @ ( implies @ SV2 @ SV9 ) @ ( implies @ ( implies @ SV9 @ SY24 ) @ ( implies @ SV2 @ SY24 ) ) )
= truth ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV10: $i,SV3: $i] :
( ( ( implies @ ( implies @ SV3 @ SV10 ) @ SV10 )
= ( implies @ ( implies @ SV10 @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV11: $i,SV4: $i] :
( ( ( implies @ ( implies @ ( not @ SV4 ) @ ( not @ SV11 ) ) @ ( implies @ SV11 @ SV4 ) )
= truth )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV12: $i,SV5: $i] :
( ( ( big_V @ SV5 @ SV12 )
= ( implies @ ( implies @ SV5 @ SV12 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV13: $i,SV6: $i] :
( ( ( big_hat @ SV6 @ SV13 )
= ( not @ ( big_V @ ( not @ SV6 ) @ ( not @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV14: $i,SV7: $i] :
( ( ~ ( ordered @ SV7 @ SV14 )
| ( ( implies @ SV7 @ SV14 )
= truth ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV15: $i,SV8: $i] :
( ( ( ( implies @ SV8 @ SV15 )
!= truth )
| ( ordered @ SV8 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV16: $i,SV9: $i,SV2: $i] :
( ( ( implies @ ( implies @ SV2 @ SV9 ) @ ( implies @ ( implies @ SV9 @ SV16 ) @ ( implies @ SV2 @ SV16 ) ) )
= truth )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV14: $i,SV7: $i] :
( ( ( ~ ( ordered @ SV7 @ SV14 ) )
= $true )
| ( ( ( implies @ SV7 @ SV14 )
= truth )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV15: $i,SV8: $i] :
( ( ( ( ( implies @ SV8 @ SV15 )
!= truth ) )
= $true )
| ( ( ordered @ SV8 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV14: $i,SV7: $i] :
( ( ( ordered @ SV7 @ SV14 )
= $false )
| ( ( ( implies @ SV7 @ SV14 )
= truth )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV15: $i,SV8: $i] :
( ( ( ( implies @ SV8 @ SV15 )
= truth )
= $false )
| ( ( ordered @ SV8 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,56,55,52,49,48,47,46,44,36]) ).
thf(58,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n020.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 : Sun Jul 3 18:35:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 9
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:9,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:11,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.38/0.57
% 0.38/0.57 ********************************
% 0.38/0.57 * All subproblems solved! *
% 0.38/0.57 ********************************
% 0.38/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.38/0.57
% 0.38/0.57 %**** Beginning of derivation protocol ****
% 0.38/0.57 % SZS output start CNFRefutation
% See solution above
% 0.38/0.57
% 0.38/0.57 %**** End of derivation protocol ****
% 0.38/0.57 %**** no. of clauses in derivation: 58 ****
% 0.38/0.57 %**** clause counter: 57 ****
% 0.38/0.57
% 0.38/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------