TSTP Solution File: COL074-3 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : COL074-3 : TPTP v8.1.0. Released v1.2.0.
% 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 : Fri Jul 15 00:34:45 EDT 2022
% Result : Unsatisfiable 0.11s 0.37s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 82 ( 66 unt; 11 typ; 0 def)
% Number of atoms : 203 ( 136 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 395 ( 13 ~; 14 |; 0 &; 368 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 102 ( 0 ^ 102 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_abstraction,type,
abstraction: $i ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_eq,type,
eq: $i ).
thf(tp_k,type,
k: $i ).
thf(tp_k_projection1,type,
k_projection1: $i ).
thf(tp_k_projection2,type,
k_projection2: $i ).
thf(tp_n,type,
n: $i > $i > $i ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_projection1,type,
projection1: $i ).
thf(tp_projection2,type,
projection2: $i ).
thf(tp_s,type,
s: $i ).
thf(1,axiom,
( s
= ( apply @ eq @ ( pair @ ( apply @ k @ s ) @ ( apply @ k @ projection2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_referential) ).
thf(2,axiom,
( ( apply @ k @ projection2 )
= k_projection2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_projection2) ).
thf(3,axiom,
( ( apply @ k @ projection1 )
= k_projection1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_projection1) ).
thf(4,axiom,
projection1 != projection2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_projections) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( X = Y )
| ( ( apply @ X @ ( n @ X @ Y ) )
!= ( apply @ Y @ ( n @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( X = Y )
| ( ( apply @ eq @ ( pair @ X @ Y ) )
= projection2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
thf(7,axiom,
! [X: $i] :
( ( apply @ eq @ ( pair @ X @ X ) )
= projection1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality) ).
thf(8,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( pair @ X @ Y ) @ Z )
= ( pair @ ( apply @ X @ Z ) @ ( apply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairwise_application) ).
thf(9,axiom,
! [X: $i] :
( ( pair @ ( apply @ projection1 @ X ) @ ( apply @ projection2 @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairing) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( apply @ projection2 @ ( pair @ X @ Y ) )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection2) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( apply @ projection1 @ ( pair @ X @ Y ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection1) ).
thf(12,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(13,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,negated_conjecture,
! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ ( apply @ k @ Z ) ) @ ( apply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
thf(15,negated_conjecture,
! [X: $i,Y: $i] :
( ( apply @ ( apply @ k @ X ) @ Y )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
thf(16,plain,
$false = $false,
inference(unfold_def,[status(thm)],[13]) ).
thf(17,plain,
( ( s
= ( apply @ eq @ ( pair @ ( apply @ k @ s ) @ ( apply @ k @ projection2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ( apply @ k @ projection2 )
= k_projection2 )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ( apply @ k @ projection1 )
= k_projection1 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ( projection1 != projection2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( ( apply @ X @ ( n @ X @ Y ) )
!= ( apply @ Y @ ( n @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( ( apply @ eq @ ( pair @ X @ Y ) )
= projection2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [X: $i] :
( ( apply @ eq @ ( pair @ X @ X ) )
= projection1 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( pair @ X @ Y ) @ Z )
= ( pair @ ( apply @ X @ Z ) @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( pair @ ( apply @ projection1 @ X ) @ ( apply @ projection2 @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ projection2 @ ( pair @ X @ Y ) )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ projection1 @ ( pair @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ ( apply @ k @ Z ) ) @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ ( apply @ k @ X ) @ Y )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
( ( ( projection1 != projection2 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( ( apply @ X @ ( n @ X @ Y ) )
!= ( apply @ Y @ ( n @ X @ Y ) ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ ( apply @ k @ X ) @ Y )
= X ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ ( apply @ k @ Z ) ) @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ projection1 @ ( pair @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ projection2 @ ( pair @ X @ Y ) )
= Y ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( pair @ ( apply @ projection1 @ X ) @ ( apply @ projection2 @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( pair @ X @ Y ) @ Z )
= ( pair @ ( apply @ X @ Z ) @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(39,plain,
( ( ! [X: $i] :
( ( apply @ eq @ ( pair @ X @ X ) )
= projection1 ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( ( apply @ eq @ ( pair @ X @ Y ) )
= projection2 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] :
( ( ( apply @ X @ ( n @ X @ Y ) )
!= ( apply @ Y @ ( n @ X @ Y ) ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(42,plain,
( ( ( projection1 != projection2 ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(43,plain,
( ( ( apply @ k @ projection1 )
= k_projection1 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(44,plain,
( ( ( apply @ k @ projection2 )
= k_projection2 )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(45,plain,
( ( s
= ( apply @ eq @ ( pair @ ( apply @ k @ s ) @ ( apply @ k @ projection2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(46,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(47,plain,
! [SV1: $i] :
( ( ! [SY18: $i] :
( ( apply @ ( apply @ k @ SV1 ) @ SY18 )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(48,plain,
! [SV2: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ SV2 ) @ SY19 ) @ SY20 )
= ( apply @ ( apply @ SV2 @ ( apply @ k @ SY20 ) ) @ ( apply @ SY19 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(49,plain,
! [SV3: $i] :
( ( ! [SY21: $i] :
( ( apply @ projection1 @ ( pair @ SV3 @ SY21 ) )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(50,plain,
! [SV4: $i] :
( ( ! [SY22: $i] :
( ( apply @ projection2 @ ( pair @ SV4 @ SY22 ) )
= SY22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(51,plain,
! [SV5: $i] :
( ( ( pair @ ( apply @ projection1 @ SV5 ) @ ( apply @ projection2 @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(52,plain,
! [SV6: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ( apply @ ( pair @ SV6 @ SY23 ) @ SY24 )
= ( pair @ ( apply @ SV6 @ SY24 ) @ ( apply @ SY23 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(53,plain,
! [SV7: $i] :
( ( ( apply @ eq @ ( pair @ SV7 @ SV7 ) )
= projection1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
! [SV8: $i] :
( ( ! [SY25: $i] :
( ( SV8 = SY25 )
| ( ( apply @ eq @ ( pair @ SV8 @ SY25 ) )
= projection2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(55,plain,
! [SV9: $i] :
( ( ! [SY26: $i] :
( ( ( apply @ SV9 @ ( n @ SV9 @ SY26 ) )
!= ( apply @ SY26 @ ( n @ SV9 @ SY26 ) ) )
| ( SV9 = SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(56,plain,
( ( projection1 = projection2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(57,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(58,plain,
! [SV10: $i,SV1: $i] :
( ( ( apply @ ( apply @ k @ SV1 ) @ SV10 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(59,plain,
! [SV11: $i,SV2: $i] :
( ( ! [SY27: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ SV2 ) @ SV11 ) @ SY27 )
= ( apply @ ( apply @ SV2 @ ( apply @ k @ SY27 ) ) @ ( apply @ SV11 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(60,plain,
! [SV12: $i,SV3: $i] :
( ( ( apply @ projection1 @ ( pair @ SV3 @ SV12 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(61,plain,
! [SV13: $i,SV4: $i] :
( ( ( apply @ projection2 @ ( pair @ SV4 @ SV13 ) )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(62,plain,
! [SV14: $i,SV6: $i] :
( ( ! [SY28: $i] :
( ( apply @ ( pair @ SV6 @ SV14 ) @ SY28 )
= ( pair @ ( apply @ SV6 @ SY28 ) @ ( apply @ SV14 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV15: $i,SV8: $i] :
( ( ( SV8 = SV15 )
| ( ( apply @ eq @ ( pair @ SV8 @ SV15 ) )
= projection2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV16: $i,SV9: $i] :
( ( ( ( apply @ SV9 @ ( n @ SV9 @ SV16 ) )
!= ( apply @ SV16 @ ( n @ SV9 @ SV16 ) ) )
| ( SV9 = SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV17: $i,SV11: $i,SV2: $i] :
( ( ( apply @ ( apply @ ( apply @ abstraction @ SV2 ) @ SV11 ) @ SV17 )
= ( apply @ ( apply @ SV2 @ ( apply @ k @ SV17 ) ) @ ( apply @ SV11 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( apply @ ( pair @ SV6 @ SV14 ) @ SV18 )
= ( pair @ ( apply @ SV6 @ SV18 ) @ ( apply @ SV14 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV15: $i,SV8: $i] :
( ( ( SV8 = SV15 )
= $true )
| ( ( ( apply @ eq @ ( pair @ SV8 @ SV15 ) )
= projection2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV16: $i,SV9: $i] :
( ( ( ( ( apply @ SV9 @ ( n @ SV9 @ SV16 ) )
!= ( apply @ SV16 @ ( n @ SV9 @ SV16 ) ) ) )
= $true )
| ( ( SV9 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV16: $i,SV9: $i] :
( ( ( ( apply @ SV9 @ ( n @ SV9 @ SV16 ) )
= ( apply @ SV16 @ ( n @ SV9 @ SV16 ) ) )
= $false )
| ( ( SV9 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(70,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[43,69,67,66,65,61,60,58,57,56,53,51,45,44]) ).
thf(71,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COL074-3 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.11 % 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 : Tue May 31 06:25:43 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.11/0.32
% 0.11/0.32 No.of.Axioms: 13
% 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:13,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:15,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.11/0.37
% 0.11/0.37 ********************************
% 0.11/0.37 * All subproblems solved! *
% 0.11/0.37 ********************************
% 0.11/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:70,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.37
% 0.11/0.37 %**** Beginning of derivation protocol ****
% 0.11/0.37 % SZS output start CNFRefutation
% See solution above
% 0.11/0.37
% 0.11/0.37 %**** End of derivation protocol ****
% 0.11/0.37 %**** no. of clauses in derivation: 71 ****
% 0.11/0.37 %**** clause counter: 70 ****
% 0.11/0.37
% 0.11/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:70,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------