TSTP Solution File: SYO268^5 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO268^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.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 17:33:05 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 38 unt; 8 typ; 0 def)
% Number of atoms : 147 ( 49 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 256 ( 39 ~; 15 |; 4 &; 183 @)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 0 ^ 72 !; 24 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_r,type,
r: a > b > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: ( a > b ) > a ).
thf(tp_sK2_Xy,type,
sK2_Xy: a > b ).
thf(tp_sK3_Xx,type,
sK3_Xx: a ).
thf(tp_sK4_Xf,type,
sK4_Xf: a > b ).
thf(tp_sK5_Xj,type,
sK5_Xj: ( b > $o ) > b ).
thf(1,conjecture,
( ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xx: b] : ( Xp @ Xx )
=> ( Xp @ ( Xj @ Xp ) ) )
=> ( ! [Xx: a] :
? [Xy: b] : ( r @ Xx @ Xy )
<=> ? [Xf: a > b] :
! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5308) ).
thf(2,negated_conjecture,
( ( ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xx: b] : ( Xp @ Xx )
=> ( Xp @ ( Xj @ Xp ) ) )
=> ( ! [Xx: a] :
? [Xy: b] : ( r @ Xx @ Xy )
<=> ? [Xf: a > b] :
! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xx: b] : ( Xp @ Xx )
=> ( Xp @ ( Xj @ Xp ) ) )
=> ( ! [Xx: a] :
? [Xy: b] : ( r @ Xx @ Xy )
<=> ? [Xf: a > b] :
! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xx: b] : ( Xp @ Xx )
=> ( Xp @ ( Xj @ Xp ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] :
? [Xy: b] : ( r @ Xx @ Xy )
<=> ? [Xf: a > b] :
! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: a] :
? [Xy: b] : ( r @ Xx @ Xy )
=> ? [Xf: a > b] :
! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(7,plain,
( ( ? [Xf: a > b] :
! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) )
=> ! [Xx: a] :
? [Xy: b] : ( r @ Xx @ Xy ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(8,plain,
( ( ~ ( ! [Xx: a] :
? [Xy: b] : ( r @ Xx @ Xy )
=> ? [Xf: a > b] :
! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ? [Xf: a > b] :
! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) )
=> ! [Xx: a] :
? [Xy: b] : ( r @ Xx @ Xy ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [Xx: a] : ( r @ Xx @ ( sK2_Xy @ Xx ) )
& ! [Xf: a > b] :
~ ( r @ ( sK1_Xx @ Xf ) @ ( Xf @ ( sK1_Xx @ Xf ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(11,plain,
( ( ! [SY8: a] : ( r @ SY8 @ ( sK4_Xf @ SY8 ) )
& ! [SY7: b] :
~ ( r @ sK3_Xx @ SY7 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(12,plain,
( ( ! [SY9: b > $o] :
( ! [Xx: b] :
~ ( SY9 @ Xx )
| ( SY9 @ ( sK5_Xj @ SY9 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(13,plain,
( ( ! [SY9: b > $o] :
( ! [Xx: b] :
~ ( SY9 @ Xx )
| ( SY9 @ ( sK5_Xj @ SY9 ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [Xx: a] : ( r @ Xx @ ( sK2_Xy @ Xx ) )
& ! [Xf: a > b] :
~ ( r @ ( sK1_Xx @ Xf ) @ ( Xf @ ( sK1_Xx @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ~ ( ~ ! [SX0: a] : ( r @ SX0 @ ( sK2_Xy @ SX0 ) )
| ~ ! [SX0: a > b] :
~ ( r @ ( sK1_Xx @ SX0 ) @ ( SX0 @ ( sK1_Xx @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
! [SV1: b > $o] :
( ( ! [SY11: b] :
~ ( SV1 @ SY11 )
| ( SV1 @ ( sK5_Xj @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ! [SX0: a] : ( r @ SX0 @ ( sK2_Xy @ SX0 ) )
| ~ ! [SX0: a > b] :
~ ( r @ ( sK1_Xx @ SX0 ) @ ( SX0 @ ( sK1_Xx @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: b > $o] :
( ( ( ! [SY11: b] :
~ ( SV1 @ SY11 ) )
= $true )
| ( ( SV1 @ ( sK5_Xj @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ! [SX0: a] : ( r @ SX0 @ ( sK2_Xy @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ! [SX0: a > b] :
~ ( r @ ( sK1_Xx @ SX0 ) @ ( SX0 @ ( sK1_Xx @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: b,SV1: b > $o] :
( ( ( ~ ( SV1 @ SV2 ) )
= $true )
| ( ( SV1 @ ( sK5_Xj @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [SX0: a] : ( r @ SX0 @ ( sK2_Xy @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [SX0: a > b] :
~ ( r @ ( sK1_Xx @ SX0 ) @ ( SX0 @ ( sK1_Xx @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: b,SV1: b > $o] :
( ( ( SV1 @ SV2 )
= $false )
| ( ( SV1 @ ( sK5_Xj @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: a] :
( ( r @ SV3 @ ( sK2_Xy @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV4: a > b] :
( ( ~ ( r @ ( sK1_Xx @ SV4 ) @ ( SV4 @ ( sK1_Xx @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV4: a > b] :
( ( r @ ( sK1_Xx @ SV4 ) @ ( SV4 @ ( sK1_Xx @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(28,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,27,25]) ).
thf(29,plain,
( ( ! [SY9: b > $o] :
( ! [Xx: b] :
~ ( SY9 @ Xx )
| ( SY9 @ ( sK5_Xj @ SY9 ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(30,plain,
( ( ! [SY8: a] : ( r @ SY8 @ ( sK4_Xf @ SY8 ) )
& ! [SY7: b] :
~ ( r @ sK3_Xx @ SY7 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(31,plain,
( ( ~ ( ~ ! [SX0: a] : ( r @ SX0 @ ( sK4_Xf @ SX0 ) )
| ~ ! [SX0: b] :
~ ( r @ sK3_Xx @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
! [SV5: b > $o] :
( ( ! [SY12: b] :
~ ( SV5 @ SY12 )
| ( SV5 @ ( sK5_Xj @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ~ ! [SX0: a] : ( r @ SX0 @ ( sK4_Xf @ SX0 ) )
| ~ ! [SX0: b] :
~ ( r @ sK3_Xx @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV5: b > $o] :
( ( ( ! [SY12: b] :
~ ( SV5 @ SY12 ) )
= $true )
| ( ( SV5 @ ( sK5_Xj @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ! [SX0: a] : ( r @ SX0 @ ( sK4_Xf @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ! [SX0: b] :
~ ( r @ sK3_Xx @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV6: b,SV5: b > $o] :
( ( ( ~ ( SV5 @ SV6 ) )
= $true )
| ( ( SV5 @ ( sK5_Xj @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
( ( ! [SX0: a] : ( r @ SX0 @ ( sK4_Xf @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ! [SX0: b] :
~ ( r @ sK3_Xx @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV6: b,SV5: b > $o] :
( ( ( SV5 @ SV6 )
= $false )
| ( ( SV5 @ ( sK5_Xj @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV7: a] :
( ( r @ SV7 @ ( sK4_Xf @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV8: b] :
( ( ~ ( r @ sK3_Xx @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV8: b] :
( ( r @ sK3_Xx @ SV8 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,43,41]) ).
thf(45,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[44,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO268^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n008.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 Jul 9 08:29:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 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: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)..
% 0.19/0.40
% 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: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:44,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: 45 ****
% 0.19/0.40 %**** clause counter: 44 ****
% 0.19/0.40
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox/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:44,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------