TSTP Solution File: COL003-4 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : COL003-4 : 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 : n019.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 00:34:31 EDT 2022
% Result : Unsatisfiable 12.94s 13.14s
% Output : CNFRefutation 12.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 27 unt; 5 typ; 0 def)
% Number of atoms : 89 ( 44 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 227 ( 11 ~; 7 |; 0 &; 209 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 0 ^ 35 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_fixed_point,type,
fixed_point: $i > $o ).
thf(tp_fixed_pt,type,
fixed_pt: $i ).
thf(tp_w,type,
w: $i ).
thf(1,axiom,
! [Strong_fixed_point: $i] :
( ( ( apply @ Strong_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( apply @ Strong_fixed_point @ fixed_pt ) ) )
| ( fixed_point @ Strong_fixed_point ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( apply @ ( apply @ w @ X ) @ Y )
= ( apply @ ( apply @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ b @ X ) @ Y ) @ Z )
= ( apply @ X @ ( apply @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
thf(4,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(5,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,negated_conjecture,
~ ( fixed_point @ ( apply @ ( apply @ b @ ( apply @ ( apply @ b @ ( apply @ w @ w ) ) @ ( apply @ ( apply @ b @ w ) @ b ) ) ) @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
thf(7,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [Strong_fixed_point: $i] :
( ( ( apply @ Strong_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( apply @ Strong_fixed_point @ fixed_pt ) ) )
| ( fixed_point @ Strong_fixed_point ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ ( apply @ w @ X ) @ Y )
= ( apply @ ( apply @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ b @ X ) @ Y ) @ Z )
= ( apply @ X @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ~ ( fixed_point @ ( apply @ ( apply @ b @ ( apply @ ( apply @ b @ ( apply @ w @ w ) ) @ ( apply @ ( apply @ b @ w ) @ b ) ) ) @ b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Strong_fixed_point: $i] :
( ( ( apply @ Strong_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( apply @ Strong_fixed_point @ fixed_pt ) ) )
| ( fixed_point @ Strong_fixed_point ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( ~ ( fixed_point @ ( apply @ ( apply @ b @ ( apply @ ( apply @ b @ ( apply @ w @ w ) ) @ ( apply @ ( apply @ b @ w ) @ b ) ) ) @ b ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ b @ X ) @ Y ) @ Z )
= ( apply @ X @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ ( apply @ w @ X ) @ Y )
= ( apply @ ( apply @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [Strong_fixed_point: $i] :
( ( ( apply @ Strong_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( apply @ Strong_fixed_point @ fixed_pt ) ) )
| ( fixed_point @ Strong_fixed_point ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(18,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
( ( fixed_point @ ( apply @ ( apply @ b @ ( apply @ ( apply @ b @ ( apply @ w @ w ) ) @ ( apply @ ( apply @ b @ w ) @ b ) ) ) @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(20,plain,
! [SV1: $i] :
( ( ! [SY6: $i,SY7: $i] :
( ( apply @ ( apply @ ( apply @ b @ SV1 ) @ SY6 ) @ SY7 )
= ( apply @ SV1 @ ( apply @ SY6 @ SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV2: $i] :
( ( ! [SY8: $i] :
( ( apply @ ( apply @ w @ SV2 ) @ SY8 )
= ( apply @ ( apply @ SV2 @ SY8 ) @ SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV3: $i] :
( ( ( ( apply @ SV3 @ fixed_pt )
!= ( apply @ fixed_pt @ ( apply @ SV3 @ fixed_pt ) ) )
| ( fixed_point @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY9: $i] :
( ( apply @ ( apply @ ( apply @ b @ SV1 ) @ SV4 ) @ SY9 )
= ( apply @ SV1 @ ( apply @ SV4 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV5: $i,SV2: $i] :
( ( ( apply @ ( apply @ w @ SV2 ) @ SV5 )
= ( apply @ ( apply @ SV2 @ SV5 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV3: $i] :
( ( ( ( ( apply @ SV3 @ fixed_pt )
!= ( apply @ fixed_pt @ ( apply @ SV3 @ fixed_pt ) ) ) )
= $true )
| ( ( fixed_point @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV6: $i,SV4: $i,SV1: $i] :
( ( ( apply @ ( apply @ ( apply @ b @ SV1 ) @ SV4 ) @ SV6 )
= ( apply @ SV1 @ ( apply @ SV4 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: $i] :
( ( ( ( apply @ SV3 @ fixed_pt )
= ( apply @ fixed_pt @ ( apply @ SV3 @ fixed_pt ) ) )
= $false )
| ( ( fixed_point @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,28,27,25,23]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : COL003-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue May 31 09:54:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 4
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.36 (rf:0,axioms:4,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:6,loop_count:0,foatp_calls:0,translation:fof_full).
% 12.94/13.14
% 12.94/13.14 ********************************
% 12.94/13.14 * All subproblems solved! *
% 12.94/13.14 ********************************
% 12.94/13.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
% 12.94/13.14
% 12.94/13.14 %**** Beginning of derivation protocol ****
% 12.94/13.14 % SZS output start CNFRefutation
% See solution above
% 12.94/13.14
% 12.94/13.14 %**** End of derivation protocol ****
% 12.94/13.14 %**** no. of clauses in derivation: 30 ****
% 12.94/13.14 %**** clause counter: 29 ****
% 12.94/13.14
% 12.94/13.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------