TSTP Solution File: SWW469+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWW469+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n028.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 00:50:18 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of formulae : 78 ( 42 unt; 10 typ; 0 def)
% Number of atoms : 381 ( 132 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 381 ( 163 ~; 105 |; 12 &; 87 @)
% ( 2 <=>; 12 =>; 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 : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 44 ( 0 ^ 40 !; 4 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_hoare_165779456gleton,type,
hoare_165779456gleton: $o ).
thf(tp_induct_false,type,
induct_false: $o ).
thf(tp_induct_true,type,
induct_true: $o ).
thf(tp_is_state,type,
is_state: $i > $o ).
thf(tp_sK1_T,type,
sK1_T: $i ).
thf(tp_sK2_S,type,
sK2_S: $i ).
thf(tp_sK3_SY5,type,
sK3_SY5: $i ).
thf(tp_sK4_REN,type,
sK4_REN: $o ).
thf(tp_state,type,
state: $i ).
thf(tp_undefined_state,type,
undefined_state: $i > $i ).
thf(1,axiom,
induct_true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_induct__true__def) ).
thf(2,axiom,
induct_true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_induct__trueI) ).
thf(3,axiom,
~ induct_false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_induct__false__def) ).
thf(4,axiom,
( hoare_165779456gleton
<=> ? [S: $i,T: $i] :
( ( is_state @ S )
& ( is_state @ T )
& ( S != T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
thf(5,axiom,
is_state @ ( undefined_state @ state ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Ostate) ).
thf(6,axiom,
hoare_165779456gleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(7,conjecture,
! [T: $i] :
( ( is_state @ T )
=> ~ ! [S: $i] :
( ( is_state @ S )
=> ( S = T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(8,negated_conjecture,
( ( ! [T: $i] :
( ( is_state @ T )
=> ~ ! [S: $i] :
( ( is_state @ S )
=> ( S = T ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [T: $i] :
( ( is_state @ T )
=> ~ ! [S: $i] :
( ( is_state @ S )
=> ( S = T ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
induct_true = $true,
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
induct_true = $true,
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ~ induct_false )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( hoare_165779456gleton
<=> ? [S: $i,T: $i] :
( ( is_state @ S )
& ( is_state @ T )
& ( S != T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( is_state @ ( undefined_state @ state ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
hoare_165779456gleton = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(16,plain,
( ( ( is_state @ sK1_T )
=> ~ ! [SY4: $i] :
( ( is_state @ SY4 )
=> ( SY4 = sK1_T ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(17,plain,
( ( is_state @ sK1_T )
= $true ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(18,plain,
( ( ~ ! [SY4: $i] :
( ( is_state @ SY4 )
=> ( SY4 = sK1_T ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(19,plain,
( ( ! [SY4: $i] :
( ( is_state @ SY4 )
=> ( SY4 = sK1_T ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [SY4: $i] :
( ~ ( is_state @ SY4 )
| ( SY4 = sK1_T ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(21,plain,
( ( ( ! [S: $i,T: $i] :
( ( S = T )
| ~ ( is_state @ S )
| ~ ( is_state @ T ) )
| hoare_165779456gleton )
& ( ~ hoare_165779456gleton
| sK4_REN )
& ( sK4_REN
=> ( ( sK2_S != sK3_SY5 )
& ( is_state @ sK2_S )
& ( is_state @ sK3_SY5 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(22,plain,
hoare_165779456gleton = $true,
inference(copy,[status(thm)],[15]) ).
thf(23,plain,
( ( is_state @ ( undefined_state @ state ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(24,plain,
( ( ( ! [S: $i,T: $i] :
( ( S = T )
| ~ ( is_state @ S )
| ~ ( is_state @ T ) )
| hoare_165779456gleton )
& ( ~ hoare_165779456gleton
| sK4_REN )
& ( sK4_REN
=> ( ( sK2_S != sK3_SY5 )
& ( is_state @ sK2_S )
& ( is_state @ sK3_SY5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ induct_false )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(26,plain,
induct_true = $true,
inference(copy,[status(thm)],[11]) ).
thf(27,plain,
induct_true = $true,
inference(copy,[status(thm)],[10]) ).
thf(28,plain,
( ( is_state @ sK1_T )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(29,plain,
( ( ! [SY4: $i] :
( ~ ( is_state @ SY4 )
| ( SY4 = sK1_T ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(30,plain,
( ( ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( is_state @ SX0 )
| ~ ( is_state @ SX1 ) )
| hoare_165779456gleton )
| ~ ~ ( ~ ( ~ hoare_165779456gleton
| sK4_REN )
| ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_S != sK3_SY5 ) )
| ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(31,plain,
induct_false = $false,
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV1: $i] :
( ( ~ ( is_state @ SV1 )
| ( SV1 = sK1_T ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( is_state @ SX0 )
| ~ ( is_state @ SX1 ) )
| hoare_165779456gleton )
| ~ ~ ( ~ ( ~ hoare_165779456gleton
| sK4_REN )
| ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_S != sK3_SY5 ) )
| ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV1: $i] :
( ( ( ~ ( is_state @ SV1 ) )
= $true )
| ( ( SV1 = sK1_T )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( is_state @ SX0 )
| ~ ( is_state @ SX1 ) )
| hoare_165779456gleton ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ~ ( ~ ( ~ hoare_165779456gleton
| sK4_REN )
| ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_S != sK3_SY5 ) )
| ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV1: $i] :
( ( ( is_state @ SV1 )
= $false )
| ( ( SV1 = sK1_T )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( is_state @ SX0 )
| ~ ( is_state @ SX1 ) )
| hoare_165779456gleton )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ~ ( ~ ( ~ hoare_165779456gleton
| sK4_REN )
| ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_S != sK3_SY5 ) )
| ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
( ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( is_state @ SX0 )
| ~ ( is_state @ SX1 ) ) )
= $true )
| ( hoare_165779456gleton = $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(41,plain,
( ( ~ ( ~ hoare_165779456gleton
| sK4_REN )
| ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_S != sK3_SY5 ) )
| ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( ! [SY6: $i] :
( ( SV2 = SY6 )
| ~ ( is_state @ SV2 )
| ~ ( is_state @ SY6 ) ) )
= $true )
| ( hoare_165779456gleton = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(43,plain,
( ( ~ ( ~ hoare_165779456gleton
| sK4_REN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(44,plain,
( ( ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_S != sK3_SY5 ) )
| ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: $i,SV2: $i] :
( ( ( ( SV2 = SV3 )
| ~ ( is_state @ SV2 )
| ~ ( is_state @ SV3 ) )
= $true )
| ( hoare_165779456gleton = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(46,plain,
( ( ~ hoare_165779456gleton
| sK4_REN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(47,plain,
( ( ~ sK4_REN
| ~ ( ~ ( ( sK2_S != sK3_SY5 ) )
| ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV3: $i,SV2: $i] :
( ( ( SV2 = SV3 )
= $true )
| ( ( ~ ( is_state @ SV2 )
| ~ ( is_state @ SV3 ) )
= $true )
| ( hoare_165779456gleton = $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(49,plain,
( ( ( ~ hoare_165779456gleton )
= $true )
| ( sK4_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(50,plain,
( ( ( ~ sK4_REN )
= $true )
| ( ( ~ ( ~ ( ( sK2_S != sK3_SY5 ) )
| ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( is_state @ SV2 ) )
= $true )
| ( ( ~ ( is_state @ SV3 ) )
= $true )
| ( ( SV2 = SV3 )
= $true )
| ( hoare_165779456gleton = $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(52,plain,
( ( hoare_165779456gleton = $false )
| ( sK4_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
( ( sK4_REN = $false )
| ( ( ~ ( ~ ( ( sK2_S != sK3_SY5 ) )
| ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV3: $i,SV2: $i] :
( ( ( is_state @ SV2 )
= $false )
| ( ( ~ ( is_state @ SV3 ) )
= $true )
| ( ( SV2 = SV3 )
= $true )
| ( hoare_165779456gleton = $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(55,plain,
( ( ( ~ ( ( sK2_S != sK3_SY5 ) )
| ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV2: $i,SV3: $i] :
( ( ( is_state @ SV3 )
= $false )
| ( ( is_state @ SV2 )
= $false )
| ( ( SV2 = SV3 )
= $true )
| ( hoare_165779456gleton = $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
( ( ( ~ ( ( sK2_S != sK3_SY5 ) ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(58,plain,
( ( ( ~ ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(59,plain,
( ( ( ( sK2_S != sK3_SY5 ) )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(60,plain,
( ( ( ~ ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) ) )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(61,plain,
( ( ( sK2_S = sK3_SY5 )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
( ( ( ~ ( is_state @ sK2_S )
| ~ ( is_state @ sK3_SY5 ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
( ( ( ~ ( is_state @ sK2_S ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(64,plain,
( ( ( ~ ( is_state @ sK3_SY5 ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(65,plain,
( ( ( is_state @ sK2_S )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(66,plain,
( ( ( is_state @ sK3_SY5 )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(67,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,66,65,61,56,52,37,31,28,27,26,23]) ).
thf(68,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW469+1 : TPTP v8.1.0. Released v5.3.0.
% 0.13/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n028.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 Jun 4 12:19:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.35
% 0.20/0.35 No.of.Axioms: 6
% 0.20/0.35
% 0.20/0.35 Length.of.Defs: 0
% 0.20/0.35
% 0.20/0.35 Contains.Choice.Funs: false
% 0.20/0.35 (rf:0,axioms:6,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:8,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:7,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:67,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: 68 ****
% 0.20/0.39 %**** clause counter: 67 ****
% 0.20/0.39
% 0.20/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:67,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------