TSTP Solution File: SEU890^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU890^5 : 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 : n014.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 12:15:37 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 43 unt; 10 typ; 0 def)
% Number of atoms : 279 ( 153 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 398 ( 121 ~; 58 |; 34 &; 177 @)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 63 ( 0 ^ 39 !; 24 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_c,type,
c: $tType ).
thf(tp_cF,type,
cF: b > a ).
thf(tp_cG,type,
cG: c > b ).
thf(tp_cS,type,
cS: c > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_SY4,type,
sK2_SY4: b ).
thf(tp_sK3_SY7,type,
sK3_SY7: c ).
thf(tp_sK4_SY6,type,
sK4_SY6: c ).
thf(1,conjecture,
! [Xx: a] :
( ? [Xt: b] :
( ? [Xt0: c] :
( ( cS @ Xt0 )
& ( Xt
= ( cG @ Xt0 ) ) )
& ( Xx
= ( cF @ Xt ) ) )
<=> ? [Xt: c] :
( ( cS @ Xt )
& ( Xx
= ( cF @ ( cG @ Xt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM29_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: a] :
( ? [Xt: b] :
( ? [Xt0: c] :
( ( cS @ Xt0 )
& ( Xt
= ( cG @ Xt0 ) ) )
& ( Xx
= ( cF @ Xt ) ) )
<=> ? [Xt: c] :
( ( cS @ Xt )
& ( Xx
= ( cF @ ( cG @ Xt ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: a] :
( ? [Xt: b] :
( ? [Xt0: c] :
( ( cS @ Xt0 )
& ( Xt
= ( cG @ Xt0 ) ) )
& ( Xx
= ( cF @ Xt ) ) )
<=> ? [Xt: c] :
( ( cS @ Xt )
& ( Xx
= ( cF @ ( cG @ Xt ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [SY4: b] :
( ? [Xt0: c] :
( ( cS @ Xt0 )
& ( SY4
= ( cG @ Xt0 ) ) )
& ( sK1_Xx
= ( cF @ SY4 ) ) )
<=> ? [SY6: c] :
( ( cS @ SY6 )
& ( sK1_Xx
= ( cF @ ( cG @ SY6 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ? [SY4: b] :
( ? [Xt0: c] :
( ( cS @ Xt0 )
& ( SY4
= ( cG @ Xt0 ) ) )
& ( sK1_Xx
= ( cF @ SY4 ) ) )
=> ? [SY6: c] :
( ( cS @ SY6 )
& ( sK1_Xx
= ( cF @ ( cG @ SY6 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(6,plain,
( ( ? [SY6: c] :
( ( cS @ SY6 )
& ( sK1_Xx
= ( cF @ ( cG @ SY6 ) ) ) )
=> ? [SY4: b] :
( ? [Xt0: c] :
( ( cS @ Xt0 )
& ( SY4
= ( cG @ Xt0 ) ) )
& ( sK1_Xx
= ( cF @ SY4 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(7,plain,
( ( ~ ( ? [SY4: b] :
( ? [Xt0: c] :
( ( cS @ Xt0 )
& ( SY4
= ( cG @ Xt0 ) ) )
& ( sK1_Xx
= ( cF @ SY4 ) ) )
=> ? [SY6: c] :
( ( cS @ SY6 )
& ( sK1_Xx
= ( cF @ ( cG @ SY6 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ? [SY6: c] :
( ( cS @ SY6 )
& ( sK1_Xx
= ( cF @ ( cG @ SY6 ) ) ) )
=> ? [SY4: b] :
( ? [Xt0: c] :
( ( cS @ Xt0 )
& ( SY4
= ( cG @ Xt0 ) ) )
& ( sK1_Xx
= ( cF @ SY4 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ( sK1_Xx
= ( cF @ sK2_SY4 ) )
& ( sK2_SY4
= ( cG @ sK3_SY7 ) )
& ( cS @ sK3_SY7 )
& ! [SY6: c] :
( ( sK1_Xx
!= ( cF @ ( cG @ SY6 ) ) )
| ~ ( cS @ SY6 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ( sK1_Xx
= ( cF @ ( cG @ sK4_SY6 ) ) )
& ( cS @ sK4_SY6 )
& ! [SY4: b] :
( ( sK1_Xx
!= ( cF @ SY4 ) )
| ! [Xt0: c] :
( ( SY4
!= ( cG @ Xt0 ) )
| ~ ( cS @ Xt0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(11,plain,
( ( ( sK1_Xx
= ( cF @ sK2_SY4 ) )
& ( sK2_SY4
= ( cG @ sK3_SY7 ) )
& ( cS @ sK3_SY7 )
& ! [SY6: c] :
( ( sK1_Xx
!= ( cF @ ( cG @ SY6 ) ) )
| ~ ( cS @ SY6 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ~ ( ( sK1_Xx
!= ( cF @ sK2_SY4 ) )
| ~ ~ ( ( sK2_SY4
!= ( cG @ sK3_SY7 ) )
| ~ ( cS @ sK3_SY7 ) ) )
| ~ ! [SX0: c] :
( ( sK1_Xx
!= ( cF @ ( cG @ SX0 ) ) )
| ~ ( cS @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ~ ( ( sK1_Xx
!= ( cF @ sK2_SY4 ) )
| ~ ~ ( ( sK2_SY4
!= ( cG @ sK3_SY7 ) )
| ~ ( cS @ sK3_SY7 ) ) )
| ~ ! [SX0: c] :
( ( sK1_Xx
!= ( cF @ ( cG @ SX0 ) ) )
| ~ ( cS @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ( sK1_Xx
!= ( cF @ sK2_SY4 ) )
| ~ ~ ( ( sK2_SY4
!= ( cG @ sK3_SY7 ) )
| ~ ( cS @ sK3_SY7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(15,plain,
( ( ~ ! [SX0: c] :
( ( sK1_Xx
!= ( cF @ ( cG @ SX0 ) ) )
| ~ ( cS @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ( sK1_Xx
!= ( cF @ sK2_SY4 ) )
| ~ ~ ( ( sK2_SY4
!= ( cG @ sK3_SY7 ) )
| ~ ( cS @ sK3_SY7 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SX0: c] :
( ( sK1_Xx
!= ( cF @ ( cG @ SX0 ) ) )
| ~ ( cS @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ( sK1_Xx
!= ( cF @ sK2_SY4 ) )
| ~ ~ ( ( sK2_SY4
!= ( cG @ sK3_SY7 ) )
| ~ ( cS @ sK3_SY7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV1: c] :
( ( ( sK1_Xx
!= ( cF @ ( cG @ SV1 ) ) )
| ~ ( cS @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ( sK1_Xx
!= ( cF @ sK2_SY4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ~ ( ( sK2_SY4
!= ( cG @ sK3_SY7 ) )
| ~ ( cS @ sK3_SY7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: c] :
( ( ( ( sK1_Xx
!= ( cF @ ( cG @ SV1 ) ) ) )
= $true )
| ( ( ~ ( cS @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( sK1_Xx
= ( cF @ sK2_SY4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( ( sK2_SY4
!= ( cG @ sK3_SY7 ) )
| ~ ( cS @ sK3_SY7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: c] :
( ( ( sK1_Xx
= ( cF @ ( cG @ SV1 ) ) )
= $false )
| ( ( ~ ( cS @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ( sK2_SY4
!= ( cG @ sK3_SY7 ) )
| ~ ( cS @ sK3_SY7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: c] :
( ( ( cS @ SV1 )
= $false )
| ( ( sK1_Xx
= ( cF @ ( cG @ SV1 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
( ( ( sK2_SY4
!= ( cG @ sK3_SY7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ( cS @ sK3_SY7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( sK2_SY4
= ( cG @ sK3_SY7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
( ( cS @ sK3_SY7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(32,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,31,30,27]) ).
thf(33,plain,
( ( ( sK1_Xx
= ( cF @ ( cG @ sK4_SY6 ) ) )
& ( cS @ sK4_SY6 )
& ! [SY4: b] :
( ( sK1_Xx
!= ( cF @ SY4 ) )
| ! [Xt0: c] :
( ( SY4
!= ( cG @ Xt0 ) )
| ~ ( cS @ Xt0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(34,plain,
( ( ~ ( ~ ~ ( ( sK1_Xx
!= ( cF @ ( cG @ sK4_SY6 ) ) )
| ~ ( cS @ sK4_SY6 ) )
| ~ ! [SX0: b] :
( ( sK1_Xx
!= ( cF @ SX0 ) )
| ! [SX1: c] :
( ( SX0
!= ( cG @ SX1 ) )
| ~ ( cS @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(35,plain,
( ( ~ ~ ( ( sK1_Xx
!= ( cF @ ( cG @ sK4_SY6 ) ) )
| ~ ( cS @ sK4_SY6 ) )
| ~ ! [SX0: b] :
( ( sK1_Xx
!= ( cF @ SX0 ) )
| ! [SX1: c] :
( ( SX0
!= ( cG @ SX1 ) )
| ~ ( cS @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(36,plain,
( ( ~ ~ ( ( sK1_Xx
!= ( cF @ ( cG @ sK4_SY6 ) ) )
| ~ ( cS @ sK4_SY6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(37,plain,
( ( ~ ! [SX0: b] :
( ( sK1_Xx
!= ( cF @ SX0 ) )
| ! [SX1: c] :
( ( SX0
!= ( cG @ SX1 ) )
| ~ ( cS @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(38,plain,
( ( ~ ( ( sK1_Xx
!= ( cF @ ( cG @ sK4_SY6 ) ) )
| ~ ( cS @ sK4_SY6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(39,plain,
( ( ! [SX0: b] :
( ( sK1_Xx
!= ( cF @ SX0 ) )
| ! [SX1: c] :
( ( SX0
!= ( cG @ SX1 ) )
| ~ ( cS @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(40,plain,
( ( ( sK1_Xx
!= ( cF @ ( cG @ sK4_SY6 ) ) )
| ~ ( cS @ sK4_SY6 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV2: b] :
( ( ( sK1_Xx
!= ( cF @ SV2 ) )
| ! [SY8: c] :
( ( SV2
!= ( cG @ SY8 ) )
| ~ ( cS @ SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(42,plain,
( ( ( sK1_Xx
!= ( cF @ ( cG @ sK4_SY6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(43,plain,
( ( ~ ( cS @ sK4_SY6 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV2: b] :
( ( ( ( sK1_Xx
!= ( cF @ SV2 ) ) )
= $true )
| ( ( ! [SY8: c] :
( ( SV2
!= ( cG @ SY8 ) )
| ~ ( cS @ SY8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(45,plain,
( ( sK1_Xx
= ( cF @ ( cG @ sK4_SY6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
( ( cS @ sK4_SY6 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(47,plain,
! [SV2: b] :
( ( ( sK1_Xx
= ( cF @ SV2 ) )
= $false )
| ( ( ! [SY8: c] :
( ( SV2
!= ( cG @ SY8 ) )
| ~ ( cS @ SY8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV3: c,SV2: b] :
( ( ( ( SV2
!= ( cG @ SV3 ) )
| ~ ( cS @ SV3 ) )
= $true )
| ( ( sK1_Xx
= ( cF @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV3: c,SV2: b] :
( ( ( ( SV2
!= ( cG @ SV3 ) ) )
= $true )
| ( ( ~ ( cS @ SV3 ) )
= $true )
| ( ( sK1_Xx
= ( cF @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV3: c,SV2: b] :
( ( ( SV2
= ( cG @ SV3 ) )
= $false )
| ( ( ~ ( cS @ SV3 ) )
= $true )
| ( ( sK1_Xx
= ( cF @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(51,plain,
! [SV2: b,SV3: c] :
( ( ( cS @ SV3 )
= $false )
| ( ( SV2
= ( cG @ SV3 ) )
= $false )
| ( ( sK1_Xx
= ( cF @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(52,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[45,51,46]) ).
thf(53,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[52,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU890^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 19:44:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (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).
% 0.13/0.39
% 0.13/0.39 ********************************
% 0.13/0.39 * All subproblems solved! *
% 0.13/0.39 ********************************
% 0.13/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:52,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.39
% 0.13/0.39 %**** Beginning of derivation protocol ****
% 0.13/0.39 % SZS output start CNFRefutation
% See solution above
% 0.13/0.39
% 0.13/0.39 %**** End of derivation protocol ****
% 0.13/0.39 %**** no. of clauses in derivation: 53 ****
% 0.13/0.39 %**** clause counter: 52 ****
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:52,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------