TSTP Solution File: SEV311^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEV311^5 : 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 : Tue Jul 19 17:36:08 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 27 unt; 5 typ; 0 def)
% Number of atoms : 239 ( 60 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 514 ( 93 ~; 68 |; 6 &; 303 @)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 130 ( 11 ^ 119 !; 0 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cF,type,
cF: ( a > $o ) > a > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_SY13,type,
sK2_SY13: a > $o ).
thf(tp_sK3_Xx,type,
sK3_Xx: ( a > $o ) > ( a > $o ) > a ).
thf(1,conjecture,
( ! [X: a > $o,Y: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cF @ X @ Xx )
=> ( cF @ Y @ Xx ) ) )
=> ! [Xx: a] :
( ( cF
@ ^ [Xx0: a] :
! [S: a > $o] :
( ! [Xx1: a] :
( ( cF @ S @ Xx1 )
=> ( S @ Xx1 ) )
=> ( S @ Xx0 ) )
@ Xx )
=> ! [S: a > $o] :
( ! [Xx0: a] :
( ( cF @ S @ Xx0 )
=> ( S @ Xx0 ) )
=> ( S @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM521_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o,Y: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cF @ X @ Xx )
=> ( cF @ Y @ Xx ) ) )
=> ! [Xx: a] :
( ( cF
@ ^ [Xx0: a] :
! [S: a > $o] :
( ! [Xx1: a] :
( ( cF @ S @ Xx1 )
=> ( S @ Xx1 ) )
=> ( S @ Xx0 ) )
@ Xx )
=> ! [S: a > $o] :
( ! [Xx0: a] :
( ( cF @ S @ Xx0 )
=> ( S @ Xx0 ) )
=> ( S @ Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cF @ X @ Xx )
=> ( cF @ Y @ Xx ) ) )
=> ! [Xx: a] :
( ( cF
@ ^ [Xx0: a] :
! [S: a > $o] :
( ! [Xx1: a] :
( ( cF @ S @ Xx1 )
=> ( S @ Xx1 ) )
=> ( S @ Xx0 ) )
@ Xx )
=> ! [S: a > $o] :
( ! [Xx0: a] :
( ( cF @ S @ Xx0 )
=> ( S @ Xx0 ) )
=> ( S @ Xx ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cF @ X @ Xx )
=> ( cF @ Y @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] :
( ( cF
@ ^ [Xx0: a] :
! [S: a > $o] :
( ! [Xx1: a] :
( ( cF @ S @ Xx1 )
=> ( S @ Xx1 ) )
=> ( S @ Xx0 ) )
@ Xx )
=> ! [S: a > $o] :
( ! [Xx0: a] :
( ( cF @ S @ Xx0 )
=> ( S @ Xx0 ) )
=> ( S @ Xx ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [Xx: a] :
( ( cF
@ ^ [Xx0: a] :
! [S: a > $o] :
( ! [Xx1: a] :
( ( cF @ S @ Xx1 )
=> ( S @ Xx1 ) )
=> ( S @ Xx0 ) )
@ Xx )
=> ! [S: a > $o] :
( ! [Xx0: a] :
( ( cF @ S @ Xx0 )
=> ( S @ Xx0 ) )
=> ( S @ Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( cF
@ ^ [Xx0: a] :
! [S: a > $o] :
( ! [Xx1: a] :
( ( cF @ S @ Xx1 )
=> ( S @ Xx1 ) )
=> ( S @ Xx0 ) )
@ sK1_Xx )
& ! [SY15: a] :
( ~ ( cF @ sK2_SY13 @ SY15 )
| ( sK2_SY13 @ SY15 ) )
& ~ ( sK2_SY13 @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ( ( X @ ( sK3_Xx @ Y @ X ) )
& ~ ( Y @ ( sK3_Xx @ Y @ X ) ) )
| ! [Xx: a] :
( ~ ( cF @ X @ Xx )
| ( cF @ Y @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ( ( X @ ( sK3_Xx @ Y @ X ) )
& ~ ( Y @ ( sK3_Xx @ Y @ X ) ) )
| ! [Xx: a] :
( ~ ( cF @ X @ Xx )
| ( cF @ Y @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( cF
@ ^ [Xx0: a] :
! [S: a > $o] :
( ! [Xx1: a] :
( ( cF @ S @ Xx1 )
=> ( S @ Xx1 ) )
=> ( S @ Xx0 ) )
@ sK1_Xx )
& ! [SY15: a] :
( ~ ( cF @ sK2_SY13 @ SY15 )
| ( sK2_SY13 @ SY15 ) )
& ~ ( sK2_SY13 @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ~ ( ~ ( SX0 @ ( sK3_Xx @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK3_Xx @ SX1 @ SX0 ) ) )
| ! [SX2: a] :
( ~ ( cF @ SX0 @ SX2 )
| ( cF @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ( cF
@ ^ [SX0: a] :
! [SX1: a > $o] :
( ~ ! [SX2: a] :
( ~ ( cF @ SX1 @ SX2 )
| ( SX1 @ SX2 ) )
| ( SX1 @ SX0 ) )
@ sK1_Xx )
| ~ ~ ( ~ ! [SX0: a] :
( ~ ( cF @ sK2_SY13 @ SX0 )
| ( sK2_SY13 @ SX0 ) )
| ~ ~ ( sK2_SY13 @ sK1_Xx ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: a > $o] :
( ( ! [SY16: a > $o] :
( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY16 @ SV1 ) )
| ~ ~ ( SY16 @ ( sK3_Xx @ SY16 @ SV1 ) ) )
| ! [SY17: a] :
( ~ ( cF @ SV1 @ SY17 )
| ( cF @ SY16 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( cF
@ ^ [SX0: a] :
! [SX1: a > $o] :
( ~ ! [SX2: a] :
( ~ ( cF @ SX1 @ SX2 )
| ( SX1 @ SX2 ) )
| ( SX1 @ SX0 ) )
@ sK1_Xx )
| ~ ~ ( ~ ! [SX0: a] :
( ~ ( cF @ sK2_SY13 @ SX0 )
| ( sK2_SY13 @ SX0 ) )
| ~ ~ ( sK2_SY13 @ sK1_Xx ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
| ! [SY18: a] :
( ~ ( cF @ SV1 @ SY18 )
| ( cF @ SV2 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( cF
@ ^ [SX0: a] :
! [SX1: a > $o] :
( ~ ! [SX2: a] :
( ~ ( cF @ SX1 @ SX2 )
| ( SX1 @ SX2 ) )
| ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ! [SX0: a] :
( ~ ( cF @ sK2_SY13 @ SX0 )
| ( sK2_SY13 @ SX0 ) )
| ~ ~ ( sK2_SY13 @ sK1_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) ) )
= $true )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV1 @ SY18 )
| ( cF @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( cF
@ ^ [SX0: a] :
! [SX1: a > $o] :
( ~ ! [SX2: a] :
( ~ ( cF @ SX1 @ SX2 )
| ( SX1 @ SX2 ) )
| ( SX1 @ SX0 ) )
@ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ~ ! [SX0: a] :
( ~ ( cF @ sK2_SY13 @ SX0 )
| ( sK2_SY13 @ SX0 ) )
| ~ ~ ( sK2_SY13 @ sK1_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV1 @ SY18 )
| ( cF @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ! [SX0: a] :
( ~ ( cF @ sK2_SY13 @ SX0 )
| ( sK2_SY13 @ SX0 ) )
| ~ ~ ( sK2_SY13 @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV1 @ SY18 )
| ( cF @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: a > $o,SV2: a > $o] :
( ( ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV1 @ SY18 )
| ( cF @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ! [SX0: a] :
( ~ ( cF @ sK2_SY13 @ SX0 )
| ( sK2_SY13 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ~ ( sK2_SY13 @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $true )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV1 @ SY18 )
| ( cF @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(28,plain,
! [SV1: a > $o,SV2: a > $o] :
( ( ( ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
= $true )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV1 @ SY18 )
| ( cF @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [SX0: a] :
( ~ ( cF @ sK2_SY13 @ SX0 )
| ( sK2_SY13 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ( sK2_SY13 @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV2: a > $o,SV3: a,SV1: a > $o] :
( ( ( ~ ( cF @ SV1 @ SV3 )
| ( cF @ SV2 @ SV3 ) )
= $true )
| ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: a > $o,SV2: a > $o] :
( ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV1 @ SY18 )
| ( cF @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV4: a] :
( ( ~ ( cF @ sK2_SY13 @ SV4 )
| ( sK2_SY13 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
( ( sK2_SY13 @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: a > $o,SV3: a,SV1: a > $o] :
( ( ( ~ ( cF @ SV1 @ SV3 ) )
= $true )
| ( ( cF @ SV2 @ SV3 )
= $true )
| ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: a > $o,SV5: a,SV1: a > $o] :
( ( ( ~ ( cF @ SV1 @ SV5 )
| ( cF @ SV2 @ SV5 ) )
= $true )
| ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV4: a] :
( ( ( ~ ( cF @ sK2_SY13 @ SV4 ) )
= $true )
| ( ( sK2_SY13 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: a > $o,SV3: a,SV1: a > $o] :
( ( ( cF @ SV1 @ SV3 )
= $false )
| ( ( cF @ SV2 @ SV3 )
= $true )
| ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV2: a > $o,SV5: a,SV1: a > $o] :
( ( ( ~ ( cF @ SV1 @ SV5 ) )
= $true )
| ( ( cF @ SV2 @ SV5 )
= $true )
| ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV4: a] :
( ( ( cF @ sK2_SY13 @ SV4 )
= $false )
| ( ( sK2_SY13 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV2: a > $o,SV5: a,SV1: a > $o] :
( ( ( cF @ SV1 @ SV5 )
= $false )
| ( ( cF @ SV2 @ SV5 )
= $true )
| ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,41,40,38,34]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV311^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Tue Jun 28 06:13:08 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34
% 0.19/0.34 No.of.Axioms: 0
% 0.19/0.34
% 0.19/0.34 Length.of.Defs: 0
% 0.19/0.34
% 0.19/0.34 Contains.Choice.Funs: false
% 0.19/0.34 (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)...
% 0.19/0.39
% 0.19/0.39 ********************************
% 0.19/0.39 * All subproblems solved! *
% 0.19/0.39 ********************************
% 0.19/0.39 % 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:42,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.39
% 0.19/0.39 %**** Beginning of derivation protocol ****
% 0.19/0.39 % SZS output start CNFRefutation
% See solution above
% 0.19/0.39
% 0.19/0.39 %**** End of derivation protocol ****
% 0.19/0.39 %**** no. of clauses in derivation: 43 ****
% 0.19/0.39 %**** clause counter: 42 ****
% 0.19/0.39
% 0.19/0.39 % 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:42,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------