TSTP Solution File: SEU783^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU783^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.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 12:14:43 EDT 2022
% Result : Theorem 0.18s 0.38s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 42 unt; 10 typ; 1 def)
% Number of atoms : 223 ( 45 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 658 ( 150 ~; 47 |; 10 &; 420 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 55 ( 0 ^ 55 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionIL,type,
binunionIL: $o ).
thf(tp_breln1,type,
breln1: $i > $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_SY20,type,
sK4_SY20: $i ).
thf(tp_sK5_SY22,type,
sK5_SY22: $i ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(1,conjecture,
( binunionIL
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIL) ).
thf(2,negated_conjecture,
( ( binunionIL
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binunionIL]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( breln1 @ sK1_A @ sK2_SY13 )
& ( breln1 @ sK1_A @ sK3_SY17 )
& ( in @ sK4_SY20 @ sK1_A )
& ( in @ sK5_SY22 @ sK1_A )
& ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
& ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( breln1 @ sK1_A @ sK2_SY13 )
& ( breln1 @ sK1_A @ sK3_SY17 )
& ( in @ sK4_SY20 @ sK1_A )
& ( in @ sK5_SY22 @ sK1_A )
& ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
& ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ ( breln1 @ sK1_A @ sK2_SY13 )
| ~ ~ ( ~ ( breln1 @ sK1_A @ sK3_SY17 )
| ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,binunionIL]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( in @ SY24 @ SV1 )
| ( in @ SY24 @ ( binunion @ SV1 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( breln1 @ sK1_A @ sK2_SY13 )
| ~ ~ ( ~ ( breln1 @ sK1_A @ sK3_SY17 )
| ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY25: $i] :
( ~ ( in @ SY25 @ SV1 )
| ( in @ SY25 @ ( binunion @ SV1 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( breln1 @ sK1_A @ sK2_SY13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ~ ( breln1 @ sK1_A @ sK3_SY17 )
| ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV1 )
| ( in @ SV3 @ ( binunion @ SV1 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( breln1 @ sK1_A @ sK2_SY13 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( ~ ( breln1 @ sK1_A @ sK3_SY17 )
| ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( ( in @ SV3 @ ( binunion @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( breln1 @ sK1_A @ sK3_SY17 )
| ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV3 @ ( binunion @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( breln1 @ sK1_A @ sK3_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( breln1 @ sK1_A @ sK3_SY17 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(28,plain,
( ( ~ ( in @ sK4_SY20 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(29,plain,
( ( ~ ~ ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(30,plain,
( ( in @ sK4_SY20 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
( ( ~ ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ( in @ sK5_SY22 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(33,plain,
( ( ~ ( in @ sK5_SY22 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(34,plain,
( ( ~ ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(35,plain,
( ( in @ sK5_SY22 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(37,plain,
( ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
| ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(38,plain,
( ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(39,plain,
( ( ~ ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(40,plain,
( ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ sK2_SY13 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( ~ ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(42,plain,
( ( in @ ( kpair @ sK4_SY20 @ sK5_SY22 ) @ ( binunion @ sK2_SY13 @ sK3_SY17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(43,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,42,40,35,30,25,22]) ).
thf(44,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU783^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jun 19 14:55:54 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34
% 0.11/0.34 No.of.Axioms: 0
% 0.11/0.34
% 0.11/0.34 Length.of.Defs: 180
% 0.11/0.34
% 0.11/0.34 Contains.Choice.Funs: false
% 0.11/0.34 (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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.18/0.38
% 0.18/0.38 ********************************
% 0.18/0.38 * All subproblems solved! *
% 0.18/0.38 ********************************
% 0.18/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:43,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.38
% 0.18/0.38 %**** Beginning of derivation protocol ****
% 0.18/0.38 % SZS output start CNFRefutation
% See solution above
% 0.18/0.38
% 0.18/0.38 %**** End of derivation protocol ****
% 0.18/0.38 %**** no. of clauses in derivation: 44 ****
% 0.18/0.38 %**** clause counter: 43 ****
% 0.18/0.38
% 0.18/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:43,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------