TSTP Solution File: SYN078+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n006.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 21 08:23:24 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 44 unt; 5 typ; 0 def)
% Number of atoms : 265 ( 91 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 381 ( 120 ~; 55 |; 17 &; 168 @)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 0 ^ 47 !; 7 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_p,type,
big_p: $i > $o ).
thf(tp_f,type,
f: $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_X,type,
sK2_X: $i ).
thf(tp_sK3_SY3,type,
sK3_SY3: $i ).
thf(1,conjecture,
( ! [X: $i] :
( ? [Y: $i] :
( ( big_p @ Y )
& ( X
= ( f @ Y ) ) )
=> ( big_p @ X ) )
<=> ! [U: $i] :
( ( big_p @ U )
=> ( big_p @ ( f @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel56) ).
thf(2,negated_conjecture,
( ( ! [X: $i] :
( ? [Y: $i] :
( ( big_p @ Y )
& ( X
= ( f @ Y ) ) )
=> ( big_p @ X ) )
<=> ! [U: $i] :
( ( big_p @ U )
=> ( big_p @ ( f @ U ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: $i] :
( ? [Y: $i] :
( ( big_p @ Y )
& ( X
= ( f @ Y ) ) )
=> ( big_p @ X ) )
<=> ! [U: $i] :
( ( big_p @ U )
=> ( big_p @ ( f @ U ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: $i] :
( ? [Y: $i] :
( ( big_p @ Y )
& ( X
= ( f @ Y ) ) )
=> ( big_p @ X ) )
=> ! [U: $i] :
( ( big_p @ U )
=> ( big_p @ ( f @ U ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ! [U: $i] :
( ( big_p @ U )
=> ( big_p @ ( f @ U ) ) )
=> ! [X: $i] :
( ? [Y: $i] :
( ( big_p @ Y )
& ( X
= ( f @ Y ) ) )
=> ( big_p @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ~ ( ! [X: $i] :
( ? [Y: $i] :
( ( big_p @ Y )
& ( X
= ( f @ Y ) ) )
=> ( big_p @ X ) )
=> ! [U: $i] :
( ( big_p @ U )
=> ( big_p @ ( f @ U ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ( ! [U: $i] :
( ( big_p @ U )
=> ( big_p @ ( f @ U ) ) )
=> ! [X: $i] :
( ? [Y: $i] :
( ( big_p @ Y )
& ( X
= ( f @ Y ) ) )
=> ( big_p @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ( X
!= ( f @ Y ) )
| ~ ( big_p @ Y ) )
| ( big_p @ X ) )
& ( big_p @ sK1_U )
& ~ ( big_p @ ( f @ sK1_U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(9,plain,
( ( ! [U: $i] :
( ~ ( big_p @ U )
| ( big_p @ ( f @ U ) ) )
& ( sK2_X
= ( f @ sK3_SY3 ) )
& ( big_p @ sK3_SY3 )
& ~ ( big_p @ sK2_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ( X
!= ( f @ Y ) )
| ~ ( big_p @ Y ) )
| ( big_p @ X ) )
& ( big_p @ sK1_U )
& ~ ( big_p @ ( f @ sK1_U ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( f @ SX1 ) )
| ~ ( big_p @ SX1 ) )
| ( big_p @ SX0 ) )
| ~ ~ ( ~ ( big_p @ sK1_U )
| ~ ~ ( big_p @ ( f @ sK1_U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( f @ SX1 ) )
| ~ ( big_p @ SX1 ) )
| ( big_p @ SX0 ) )
| ~ ~ ( ~ ( big_p @ sK1_U )
| ~ ~ ( big_p @ ( f @ sK1_U ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( f @ SX1 ) )
| ~ ( big_p @ SX1 ) )
| ( big_p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ~ ( big_p @ sK1_U )
| ~ ~ ( big_p @ ( f @ sK1_U ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( f @ SX1 ) )
| ~ ( big_p @ SX1 ) )
| ( big_p @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ( big_p @ sK1_U )
| ~ ~ ( big_p @ ( f @ sK1_U ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
! [SV1: $i] :
( ( ! [SY4: $i] :
( ( SV1
!= ( f @ SY4 ) )
| ~ ( big_p @ SY4 ) )
| ( big_p @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( big_p @ sK1_U )
| ~ ~ ( big_p @ ( f @ sK1_U ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV1: $i] :
( ( ( ! [SY4: $i] :
( ( SV1
!= ( f @ SY4 ) )
| ~ ( big_p @ SY4 ) ) )
= $true )
| ( ( big_p @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( big_p @ sK1_U ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ~ ( big_p @ ( f @ sK1_U ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: $i,SV1: $i] :
( ( ( ( SV1
!= ( f @ SV2 ) )
| ~ ( big_p @ SV2 ) )
= $true )
| ( ( big_p @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( big_p @ sK1_U )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( big_p @ ( f @ sK1_U ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: $i,SV1: $i] :
( ( ( ( SV1
!= ( f @ SV2 ) ) )
= $true )
| ( ( ~ ( big_p @ SV2 ) )
= $true )
| ( ( big_p @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( big_p @ ( f @ sK1_U ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV2: $i,SV1: $i] :
( ( ( SV1
= ( f @ SV2 ) )
= $false )
| ( ( ~ ( big_p @ SV2 ) )
= $true )
| ( ( big_p @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV1: $i,SV2: $i] :
( ( ( big_p @ SV2 )
= $false )
| ( ( SV1
= ( f @ SV2 ) )
= $false )
| ( ( big_p @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,28,26]) ).
thf(30,plain,
( ( ! [U: $i] :
( ~ ( big_p @ U )
| ( big_p @ ( f @ U ) ) )
& ( sK2_X
= ( f @ sK3_SY3 ) )
& ( big_p @ sK3_SY3 )
& ~ ( big_p @ sK2_X ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(31,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( big_p @ SX0 )
| ( big_p @ ( f @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ( sK2_X
!= ( f @ sK3_SY3 ) )
| ~ ( big_p @ sK3_SY3 ) )
| ~ ~ ( big_p @ sK2_X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_p @ SX0 )
| ( big_p @ ( f @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ( sK2_X
!= ( f @ sK3_SY3 ) )
| ~ ( big_p @ sK3_SY3 ) )
| ~ ~ ( big_p @ sK2_X ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(33,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_p @ SX0 )
| ( big_p @ ( f @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(34,plain,
( ( ~ ~ ( ~ ~ ( ( sK2_X
!= ( f @ sK3_SY3 ) )
| ~ ( big_p @ sK3_SY3 ) )
| ~ ~ ( big_p @ sK2_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(35,plain,
( ( ! [SX0: $i] :
( ~ ( big_p @ SX0 )
| ( big_p @ ( f @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ( ~ ~ ( ( sK2_X
!= ( f @ sK3_SY3 ) )
| ~ ( big_p @ sK3_SY3 ) )
| ~ ~ ( big_p @ sK2_X ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: $i] :
( ( ~ ( big_p @ SV3 )
| ( big_p @ ( f @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(38,plain,
( ( ~ ~ ( ( sK2_X
!= ( f @ sK3_SY3 ) )
| ~ ( big_p @ sK3_SY3 ) )
| ~ ~ ( big_p @ sK2_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV3: $i] :
( ( ( ~ ( big_p @ SV3 ) )
= $true )
| ( ( big_p @ ( f @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( ~ ~ ( ( sK2_X
!= ( f @ sK3_SY3 ) )
| ~ ( big_p @ sK3_SY3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( ~ ~ ( big_p @ sK2_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV3: $i] :
( ( ( big_p @ SV3 )
= $false )
| ( ( big_p @ ( f @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
( ( ~ ( ( sK2_X
!= ( f @ sK3_SY3 ) )
| ~ ( big_p @ sK3_SY3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ~ ( big_p @ sK2_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
( ( ( sK2_X
!= ( f @ sK3_SY3 ) )
| ~ ( big_p @ sK3_SY3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
( ( big_p @ sK2_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
( ( ( sK2_X
!= ( f @ sK3_SY3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(48,plain,
( ( ~ ( big_p @ sK3_SY3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(49,plain,
( ( sK2_X
= ( f @ sK3_SY3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(50,plain,
( ( big_p @ sK3_SY3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[42,50,49,46]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n006.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 : Mon Jul 11 12:12:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:0,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:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.40
% 0.19/0.40 ********************************
% 0.19/0.40 * All subproblems solved! *
% 0.19/0.40 ********************************
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:51,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.40
% 0.19/0.40 %**** Beginning of derivation protocol ****
% 0.19/0.40 % SZS output start CNFRefutation
% See solution above
% 0.19/0.40
% 0.19/0.40 %**** End of derivation protocol ****
% 0.19/0.40 %**** no. of clauses in derivation: 52 ****
% 0.19/0.40 %**** clause counter: 51 ****
% 0.19/0.40
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:51,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------