TSTP Solution File: ALG210+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG210+2 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.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 14 17:25:07 EDT 2022
% Result : Theorem 1.53s 1.71s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 34 unt; 6 typ; 0 def)
% Number of atoms : 240 ( 125 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 383 ( 63 ~; 48 |; 18 &; 246 @)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 0 ^ 70 !; 2 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i ).
thf(tp_sK3_SY10,type,
sK3_SY10: $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i ).
thf(tp_times,type,
times: $i > $i > $i ).
thf(1,axiom,
! [B: $i] :
( ( element @ B )
<=> ? [C: $i] :
( ( ( times @ B @ C )
= B )
& ( ( times @ B @ B )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ( times @ ( times @ A @ B ) @ C )
= ( times @ B @ ( times @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(3,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( element @ A )
& ( element @ B )
& ( C
= ( times @ A @ B ) ) )
=> ( element @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
thf(4,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ A )
& ( element @ B )
& ( C
= ( times @ A @ B ) ) )
=> ( element @ C ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ A )
& ( element @ B )
& ( C
= ( times @ A @ B ) ) )
=> ( element @ C ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [B: $i] :
( ( element @ B )
<=> ? [C: $i] :
( ( ( times @ B @ C )
= B )
& ( ( times @ B @ B )
= C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( times @ ( times @ A @ B ) @ C )
= ( times @ B @ ( times @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ! [SY8: $i,SY9: $i] :
( ( ( element @ sK1_A )
& ( element @ SY8 )
& ( SY9
= ( times @ sK1_A @ SY8 ) ) )
=> ( element @ SY9 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(9,plain,
( ( ! [SY10: $i] :
( ( ( element @ sK1_A )
& ( element @ sK2_SY8 )
& ( SY10
= ( times @ sK1_A @ sK2_SY8 ) ) )
=> ( element @ SY10 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(10,plain,
( ( ( ( element @ sK1_A )
& ( element @ sK2_SY8 )
& ( sK3_SY10
= ( times @ sK1_A @ sK2_SY8 ) ) )
=> ( element @ sK3_SY10 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(11,plain,
( ( element @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(12,plain,
( ( element @ sK2_SY8 )
= $true ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(13,plain,
( ( sK3_SY10
= ( times @ sK1_A @ sK2_SY8 ) )
= $true ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(14,plain,
( ( element @ sK3_SY10 )
= $false ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(15,plain,
( ( ~ ( element @ sK3_SY10 ) )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [B: $i] :
( ! [C: $i] :
( ( ( times @ B @ C )
!= B )
| ( ( times @ B @ B )
!= C ) )
| ( element @ B ) )
& ! [B: $i] :
( ~ ( element @ B )
| ( ( ( times @ B @ ( sK4_C @ B ) )
= B )
& ( ( times @ B @ B )
= ( sK4_C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( times @ ( times @ A @ B ) @ C )
= ( times @ B @ ( times @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(18,plain,
( ( ! [B: $i] :
( ! [C: $i] :
( ( ( times @ B @ C )
!= B )
| ( ( times @ B @ B )
!= C ) )
| ( element @ B ) )
& ! [B: $i] :
( ~ ( element @ B )
| ( ( ( times @ B @ ( sK4_C @ B ) )
= B )
& ( ( times @ B @ B )
= ( sK4_C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(19,plain,
( ( sK3_SY10
= ( times @ sK1_A @ sK2_SY8 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( element @ sK2_SY8 )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( element @ sK1_A )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ ( element @ sK3_SY10 ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(23,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( ( times @ SX0 @ SX1 )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= SX1 ) )
| ( element @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 )
| ~ ( ( ( times @ SX0 @ ( sK4_C @ SX0 ) )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= ( sK4_C @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(24,plain,
! [SV1: $i] :
( ( ! [SY11: $i,SY12: $i] :
( ( times @ ( times @ SV1 @ SY11 ) @ SY12 )
= ( times @ SY11 @ ( times @ SY12 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(25,plain,
( ( element @ sK3_SY10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( ( times @ SX0 @ SX1 )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= SX1 ) )
| ( element @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 )
| ~ ( ( ( times @ SX0 @ ( sK4_C @ SX0 ) )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= ( sK4_C @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY13: $i] :
( ( times @ ( times @ SV1 @ SV2 ) @ SY13 )
= ( times @ SV2 @ ( times @ SY13 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( ( times @ SX0 @ SX1 )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= SX1 ) )
| ( element @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 )
| ~ ( ( ( times @ SX0 @ ( sK4_C @ SX0 ) )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= ( sK4_C @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( times @ ( times @ SV1 @ SV2 ) @ SV3 )
= ( times @ SV2 @ ( times @ SV3 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( ( times @ SX0 @ SX1 )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= SX1 ) )
| ( element @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 )
| ~ ( ( ( times @ SX0 @ ( sK4_C @ SX0 ) )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= ( sK4_C @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV4: $i] :
( ( ! [SY14: $i] :
( ( ( times @ SV4 @ SY14 )
!= SV4 )
| ( ( times @ SV4 @ SV4 )
!= SY14 ) )
| ( element @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV5: $i] :
( ( ~ ( element @ SV5 )
| ~ ( ( ( times @ SV5 @ ( sK4_C @ SV5 ) )
!= SV5 )
| ( ( times @ SV5 @ SV5 )
!= ( sK4_C @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV4: $i] :
( ( ( ! [SY14: $i] :
( ( ( times @ SV4 @ SY14 )
!= SV4 )
| ( ( times @ SV4 @ SV4 )
!= SY14 ) ) )
= $true )
| ( ( element @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV5: $i] :
( ( ( ~ ( element @ SV5 ) )
= $true )
| ( ( ~ ( ( ( times @ SV5 @ ( sK4_C @ SV5 ) )
!= SV5 )
| ( ( times @ SV5 @ SV5 )
!= ( sK4_C @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV6: $i,SV4: $i] :
( ( ( ( ( times @ SV4 @ SV6 )
!= SV4 )
| ( ( times @ SV4 @ SV4 )
!= SV6 ) )
= $true )
| ( ( element @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV5: $i] :
( ( ( element @ SV5 )
= $false )
| ( ( ~ ( ( ( times @ SV5 @ ( sK4_C @ SV5 ) )
!= SV5 )
| ( ( times @ SV5 @ SV5 )
!= ( sK4_C @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV6: $i,SV4: $i] :
( ( ( ( ( times @ SV4 @ SV6 )
!= SV4 ) )
= $true )
| ( ( ( ( times @ SV4 @ SV4 )
!= SV6 ) )
= $true )
| ( ( element @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV5: $i] :
( ( ( ( ( times @ SV5 @ ( sK4_C @ SV5 ) )
!= SV5 )
| ( ( times @ SV5 @ SV5 )
!= ( sK4_C @ SV5 ) ) )
= $false )
| ( ( element @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV6: $i,SV4: $i] :
( ( ( ( times @ SV4 @ SV6 )
= SV4 )
= $false )
| ( ( ( ( times @ SV4 @ SV4 )
!= SV6 ) )
= $true )
| ( ( element @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV5: $i] :
( ( ( ( ( times @ SV5 @ ( sK4_C @ SV5 ) )
!= SV5 ) )
= $false )
| ( ( element @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV5: $i] :
( ( ( ( ( times @ SV5 @ SV5 )
!= ( sK4_C @ SV5 ) ) )
= $false )
| ( ( element @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV6: $i,SV4: $i] :
( ( ( ( times @ SV4 @ SV4 )
= SV6 )
= $false )
| ( ( ( times @ SV4 @ SV6 )
= SV4 )
= $false )
| ( ( element @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV5: $i] :
( ( ( ( times @ SV5 @ ( sK4_C @ SV5 ) )
= SV5 )
= $true )
| ( ( element @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV5: $i] :
( ( ( ( times @ SV5 @ SV5 )
= ( sK4_C @ SV5 ) )
= $true )
| ( ( element @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(47,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,46,45,44,30,25,21,20]) ).
thf(48,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG210+2 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 8 22:43:12 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 2
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:2,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:4,loop_count:0,foatp_calls:0,translation:fof_full)..
% 1.53/1.71
% 1.53/1.71 ********************************
% 1.53/1.71 * All subproblems solved! *
% 1.53/1.71 ********************************
% 1.53/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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)
% 1.53/1.71
% 1.53/1.71 %**** Beginning of derivation protocol ****
% 1.53/1.71 % SZS output start CNFRefutation
% See solution above
% 1.53/1.71
% 1.53/1.71 %**** End of derivation protocol ****
% 1.53/1.71 %**** no. of clauses in derivation: 48 ****
% 1.53/1.71 %**** clause counter: 47 ****
% 1.53/1.71
% 1.53/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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)
%------------------------------------------------------------------------------