TSTP Solution File: SYN066+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN066+1 : TPTP v8.1.0. Bugfixed v3.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.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 08:23:14 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 35 unt; 8 typ; 0 def)
% Number of atoms : 216 ( 53 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 476 ( 67 ~; 46 |; 8 &; 347 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 103 ( 0 ^ 86 !; 17 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_p,type,
big_p: $i > $i > $o ).
thf(tp_big_q,type,
big_q: $i > $i > $o ).
thf(tp_big_r,type,
big_r: $i > $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_Y,type,
sK2_Y: $i > $i > $i ).
thf(tp_sK3_W,type,
sK3_W: $i > $i ).
thf(tp_sK4_SY15,type,
sK4_SY15: $i > $i > $i ).
thf(tp_sK5_SY16,type,
sK5_SY16: $i > $i > $i ).
thf(1,axiom,
( ? [X: $i,Y: $i] : ( big_q @ X @ Y )
=> ! [Z: $i] : ( big_r @ Z @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37_3) ).
thf(2,axiom,
! [X: $i,Z: $i] :
( ~ ( big_p @ X @ Z )
=> ? [Y: $i] : ( big_q @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37_2) ).
thf(3,axiom,
! [Z: $i] :
? [W: $i] :
! [X: $i] :
? [Y: $i] :
( ( ( big_p @ X @ Z )
=> ( big_p @ Y @ W ) )
& ( big_p @ Y @ Z )
& ( ( big_p @ Y @ W )
=> ? [U: $i] : ( big_q @ U @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37_1) ).
thf(4,conjecture,
! [X: $i] :
? [Y: $i] : ( big_r @ X @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37) ).
thf(5,negated_conjecture,
( ( ! [X: $i] :
? [Y: $i] : ( big_r @ X @ Y ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [X: $i] :
? [Y: $i] : ( big_r @ X @ Y ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ? [X: $i,Y: $i] : ( big_q @ X @ Y )
=> ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [X: $i,Z: $i] :
( ~ ( big_p @ X @ Z )
=> ? [Y: $i] : ( big_q @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [Z: $i] :
? [W: $i] :
! [X: $i] :
? [Y: $i] :
( ( ( big_p @ X @ Z )
=> ( big_p @ Y @ W ) )
& ( big_p @ Y @ Z )
& ( ( big_p @ Y @ W )
=> ? [U: $i] : ( big_q @ U @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ? [SY13: $i] : ( big_r @ sK1_X @ SY13 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(11,plain,
( ( ~ ? [SY13: $i] : ( big_r @ sK1_X @ SY13 ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [SY13: $i] :
~ ( big_r @ sK1_X @ SY13 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i] :
~ ( big_q @ X @ Y )
| ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(14,plain,
( ( ! [X: $i,Z: $i] :
( ( big_p @ X @ Z )
| ( big_q @ ( sK2_Y @ Z @ X ) @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(15,plain,
( ( ! [Z: $i,SY14: $i] :
( ( ~ ( big_p @ SY14 @ Z )
| ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ ( sK3_W @ Z ) ) )
& ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ Z )
& ( ~ ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ ( sK3_W @ Z ) )
| ( big_q @ ( sK5_SY16 @ SY14 @ Z ) @ ( sK3_W @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(16,plain,
( ( ! [Z: $i,SY14: $i] :
( ( ~ ( big_p @ SY14 @ Z )
| ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ ( sK3_W @ Z ) ) )
& ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ Z )
& ( ~ ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ ( sK3_W @ Z ) )
| ( big_q @ ( sK5_SY16 @ SY14 @ Z ) @ ( sK3_W @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [X: $i,Z: $i] :
( ( big_p @ X @ Z )
| ( big_q @ ( sK2_Y @ Z @ X ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
~ ( big_q @ X @ Y )
| ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( ! [SY13: $i] :
~ ( big_r @ sK1_X @ SY13 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ( ~ ( big_p @ SX1 @ SX0 )
| ( big_p @ ( sK4_SY15 @ SX1 @ SX0 ) @ ( sK3_W @ SX0 ) ) )
| ~ ( big_p @ ( sK4_SY15 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( big_p @ ( sK4_SY15 @ SX1 @ SX0 ) @ ( sK3_W @ SX0 ) )
| ( big_q @ ( sK5_SY16 @ SX1 @ SX0 ) @ ( sK3_W @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(21,plain,
! [SV1: $i] :
( ( ! [SY18: $i] :
( ( big_p @ SV1 @ SY18 )
| ( big_q @ ( sK2_Y @ SY18 @ SV1 ) @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
( ( ( ! [X: $i,Y: $i] :
~ ( big_q @ X @ Y ) )
= $true )
| ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: $i] :
( ( ~ ( big_r @ sK1_X @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY19: $i] :
~ ( ~ ~ ( ~ ( ~ ( big_p @ SY19 @ SV3 )
| ( big_p @ ( sK4_SY15 @ SY19 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
| ~ ( big_p @ ( sK4_SY15 @ SY19 @ SV3 ) @ SV3 ) )
| ~ ( ~ ( big_p @ ( sK4_SY15 @ SY19 @ SV3 ) @ ( sK3_W @ SV3 ) )
| ( big_q @ ( sK5_SY16 @ SY19 @ SV3 ) @ ( sK3_W @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV4: $i,SV1: $i] :
( ( ( big_p @ SV1 @ SV4 )
| ( big_q @ ( sK2_Y @ SV4 @ SV1 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV5: $i] :
( ( ( ! [SY20: $i] :
~ ( big_q @ SV5 @ SY20 ) )
= $true )
| ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: $i] :
( ( big_r @ sK1_X @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( big_p @ SV6 @ SV3 )
| ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
| ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) )
| ~ ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
| ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV4: $i,SV1: $i] :
( ( ( big_p @ SV1 @ SV4 )
= $true )
| ( ( big_q @ ( sK2_Y @ SV4 @ SV1 ) @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ( big_q @ SV5 @ SV7 ) )
= $true )
| ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ~ ( ~ ( ~ ( big_p @ SV6 @ SV3 )
| ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
| ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) )
| ~ ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
| ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV7: $i,SV5: $i] :
( ( ( big_q @ SV5 @ SV7 )
= $false )
| ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ~ ( ~ ( ~ ( big_p @ SV6 @ SV3 )
| ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
| ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(34,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
| ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV7: $i,SV5: $i,SV8: $i] :
( ( ( big_r @ SV8 @ SV8 )
= $true )
| ( ( big_q @ SV5 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( big_p @ SV6 @ SV3 )
| ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
| ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
| ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ( big_p @ SV6 @ SV3 )
| ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
| ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
= $true )
| ( ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ( big_p @ SV6 @ SV3 )
| ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV3: $i,SV6: $i] :
( ( ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
= $false )
| ( ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( big_p @ SV6 @ SV3 )
| ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV3: $i,SV6: $i] :
( ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( big_p @ SV6 @ SV3 ) )
= $true )
| ( ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV3: $i,SV6: $i] :
( ( ( big_p @ SV6 @ SV3 )
= $false )
| ( ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(47,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,46,44,42,35,29]) ).
thf(48,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN066+1 : TPTP v8.1.0. Bugfixed v3.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 12 09:04:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 3
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:3,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:5,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.20/0.39
% 0.20/0.39 ********************************
% 0.20/0.39 * All subproblems solved! *
% 0.20/0.39 ********************************
% 0.20/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.39
% 0.20/0.39 %**** Beginning of derivation protocol ****
% 0.20/0.39 % SZS output start CNFRefutation
% See solution above
% 0.20/0.39
% 0.20/0.39 %**** End of derivation protocol ****
% 0.20/0.39 %**** no. of clauses in derivation: 48 ****
% 0.20/0.39 %**** clause counter: 47 ****
% 0.20/0.39
% 0.20/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------