TSTP Solution File: SEU303+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU303+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Tue Jul 19 12:09:51 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 74 ( 47 unt; 8 typ; 0 def)
% Number of atoms : 337 ( 94 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 391 ( 59 ~; 67 |; 14 &; 235 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 ^ 58 !; 2 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_A,type,
sK2_A: $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
thf(2,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(3,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(6,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(7,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(8,conjecture,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
=> ( finite @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
thf(9,negated_conjecture,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
=> ( finite @ ( relation_rng @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
=> ( finite @ ( relation_rng @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
$true = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
$true = $true,
inference(unfold_def,[status(thm)],[7]) ).
thf(18,plain,
( ( ( ( relation @ sK1_A )
& ( function @ sK1_A ) )
=> ( ( finite @ ( relation_dom @ sK1_A ) )
=> ( finite @ ( relation_rng @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(19,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(20,plain,
( ( function @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(21,plain,
( ( finite @ ( relation_dom @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(22,plain,
( ( finite @ ( relation_rng @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(23,plain,
( ( ~ ( finite @ ( relation_rng @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( finite @ A )
| ( finite @ ( relation_image @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(25,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(26,plain,
( ( ( function @ sK2_A )
& ( relation @ sK2_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( finite @ B )
| ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(28,plain,
$true = $true,
inference(copy,[status(thm)],[17]) ).
thf(29,plain,
$true = $true,
inference(copy,[status(thm)],[16]) ).
thf(30,plain,
$true = $true,
inference(copy,[status(thm)],[15]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( finite @ B )
| ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(32,plain,
( ( ( function @ sK2_A )
& ( relation @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(33,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( finite @ A )
| ( finite @ ( relation_image @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(35,plain,
( ( finite @ ( relation_dom @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(36,plain,
( ( function @ sK1_A )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(37,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(38,plain,
( ( ~ ( finite @ ( relation_rng @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(39,plain,
( ( ~ ( ~ ( function @ sK2_A )
| ~ ( relation @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(40,plain,
! [SV1: $i] :
( ( ! [SY7: $i] :
( ~ ( function @ SV1 )
| ~ ( relation @ SV1 )
| ~ ( finite @ SY7 )
| ( finite @ ( relation_image @ SV1 @ SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV2: $i] :
( ( ~ ( relation @ SV2 )
| ( ( relation_image @ SV2 @ ( relation_dom @ SV2 ) )
= ( relation_rng @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV3: $i] :
( ( ! [SY8: $i] :
( ~ ( function @ SY8 )
| ~ ( relation @ SY8 )
| ~ ( finite @ SV3 )
| ( finite @ ( relation_image @ SY8 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
( ( finite @ ( relation_rng @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( ~ ( function @ sK2_A )
| ~ ( relation @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( function @ SV1 )
| ~ ( relation @ SV1 )
| ~ ( finite @ SV4 )
| ( finite @ ( relation_image @ SV1 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV2: $i] :
( ( ( ~ ( relation @ SV2 ) )
= $true )
| ( ( ( relation_image @ SV2 @ ( relation_dom @ SV2 ) )
= ( relation_rng @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV3: $i,SV5: $i] :
( ( ~ ( function @ SV5 )
| ~ ( relation @ SV5 )
| ~ ( finite @ SV3 )
| ( finite @ ( relation_image @ SV5 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
( ( ~ ( function @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(49,plain,
( ( ~ ( relation @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( function @ SV1 )
| ~ ( relation @ SV1 )
| ~ ( finite @ SV4 ) )
= $true )
| ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV2: $i] :
( ( ( relation @ SV2 )
= $false )
| ( ( ( relation_image @ SV2 @ ( relation_dom @ SV2 ) )
= ( relation_rng @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV3: $i,SV5: $i] :
( ( ( ~ ( function @ SV5 )
| ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( finite @ SV3 )
| ( finite @ ( relation_image @ SV5 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
( ( function @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
( ( relation @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(55,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( function @ SV1 )
| ~ ( relation @ SV1 ) )
= $true )
| ( ( ~ ( finite @ SV4 ) )
= $true )
| ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV3: $i,SV5: $i] :
( ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( finite @ SV3 )
| ( finite @ ( relation_image @ SV5 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( function @ SV1 ) )
= $true )
| ( ( ~ ( relation @ SV1 ) )
= $true )
| ( ( ~ ( finite @ SV4 ) )
= $true )
| ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV3: $i,SV5: $i] :
( ( ( function @ SV5 )
= $false )
| ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( finite @ SV3 )
| ( finite @ ( relation_image @ SV5 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV4: $i,SV1: $i] :
( ( ( function @ SV1 )
= $false )
| ( ( ~ ( relation @ SV1 ) )
= $true )
| ( ( ~ ( finite @ SV4 ) )
= $true )
| ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV3: $i,SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false )
| ( ( ~ ( finite @ SV3 )
| ( finite @ ( relation_image @ SV5 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV4: $i,SV1: $i] :
( ( ( relation @ SV1 )
= $false )
| ( ( function @ SV1 )
= $false )
| ( ( ~ ( finite @ SV4 ) )
= $true )
| ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( finite @ SV3 ) )
= $true )
| ( ( finite @ ( relation_image @ SV5 @ SV3 ) )
= $true )
| ( ( function @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV1: $i,SV4: $i] :
( ( ( finite @ SV4 )
= $false )
| ( ( function @ SV1 )
= $false )
| ( ( relation @ SV1 )
= $false )
| ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV5: $i,SV3: $i] :
( ( ( finite @ SV3 )
= $false )
| ( ( finite @ ( relation_image @ SV5 @ SV3 ) )
= $true )
| ( ( function @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,64,63,54,53,51,43,37,36,35,30,29]) ).
thf(66,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU303+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n019.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 : Sat Jun 18 19:26:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 7
% 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:7,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:9,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.21/0.39
% 0.21/0.39 ********************************
% 0.21/0.39 * All subproblems solved! *
% 0.21/0.39 ********************************
% 0.21/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:65,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.39
% 0.21/0.39 %**** Beginning of derivation protocol ****
% 0.21/0.39 % SZS output start CNFRefutation
% See solution above
% 0.21/0.39
% 0.21/0.39 %**** End of derivation protocol ****
% 0.21/0.39 %**** no. of clauses in derivation: 66 ****
% 0.21/0.39 %**** clause counter: 65 ****
% 0.21/0.39
% 0.21/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:65,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------