TSTP Solution File: ALG210+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG210+1 : 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 : n025.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 263.03s 263.43s
% Output : CNFRefutation 263.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 36 unt; 5 typ; 0 def)
% Number of atoms : 291 ( 151 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 435 ( 63 ~; 56 |; 11 &; 298 @)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 ^ 76 !; 2 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY36,type,
sK2_SY36: $i ).
thf(tp_sK3_C,type,
sK3_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/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(3,conjecture,
! [A: $i,B: $i] :
( ( ( element @ A )
& ( element @ B ) )
=> ( element @ ( times @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
thf(4,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( element @ A )
& ( element @ B ) )
=> ( element @ ( times @ A @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i] :
( ( ( element @ A )
& ( element @ B ) )
=> ( element @ ( times @ A @ B ) ) ) )
= $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,
( ( ! [SY36: $i] :
( ( ( element @ sK1_A )
& ( element @ SY36 ) )
=> ( element @ ( times @ sK1_A @ SY36 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(9,plain,
( ( ( ( element @ sK1_A )
& ( element @ sK2_SY36 ) )
=> ( element @ ( times @ sK1_A @ sK2_SY36 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(10,plain,
( ( element @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[9]) ).
thf(11,plain,
( ( element @ sK2_SY36 )
= $true ),
inference(standard_cnf,[status(thm)],[9]) ).
thf(12,plain,
( ( element @ ( times @ sK1_A @ sK2_SY36 ) )
= $false ),
inference(standard_cnf,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( element @ ( times @ sK1_A @ sK2_SY36 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [B: $i] :
( ! [C: $i] :
( ( ( times @ B @ C )
!= B )
| ( ( times @ B @ B )
!= C ) )
| ( element @ B ) )
& ! [B: $i] :
( ~ ( element @ B )
| ( ( ( times @ B @ ( sK3_C @ B ) )
= B )
& ( ( times @ B @ B )
= ( sK3_C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(15,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( times @ ( times @ A @ B ) @ C )
= ( times @ B @ ( times @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(16,plain,
( ( ! [B: $i] :
( ! [C: $i] :
( ( ( times @ B @ C )
!= B )
| ( ( times @ B @ B )
!= C ) )
| ( element @ B ) )
& ! [B: $i] :
( ~ ( element @ B )
| ( ( ( times @ B @ ( sK3_C @ B ) )
= B )
& ( ( times @ B @ B )
= ( sK3_C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(17,plain,
( ( element @ sK2_SY36 )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( element @ sK1_A )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ~ ( element @ ( times @ sK1_A @ sK2_SY36 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( ( times @ SX0 @ SX1 )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= SX1 ) )
| ( element @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 )
| ~ ( ( ( times @ SX0 @ ( sK3_C @ SX0 ) )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= ( sK3_C @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(21,plain,
! [SV1: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ( times @ ( times @ SV1 @ SY37 ) @ SY38 )
= ( times @ SY37 @ ( times @ SY38 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(22,plain,
( ( element @ ( times @ sK1_A @ sK2_SY36 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( ( times @ SX0 @ SX1 )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= SX1 ) )
| ( element @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 )
| ~ ( ( ( times @ SX0 @ ( sK3_C @ SX0 ) )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= ( sK3_C @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY39: $i] :
( ( times @ ( times @ SV1 @ SV2 ) @ SY39 )
= ( times @ SV2 @ ( times @ SY39 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( ( times @ SX0 @ SX1 )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= SX1 ) )
| ( element @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 )
| ~ ( ( ( times @ SX0 @ ( sK3_C @ SX0 ) )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= ( sK3_C @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( times @ ( times @ SV1 @ SV2 ) @ SV3 )
= ( times @ SV2 @ ( times @ SV3 @ 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 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 )
| ~ ( ( ( times @ SX0 @ ( sK3_C @ SX0 ) )
!= SX0 )
| ( ( times @ SX0 @ SX0 )
!= ( sK3_C @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV4: $i] :
( ( ! [SY40: $i] :
( ( ( times @ SV4 @ SY40 )
!= SV4 )
| ( ( times @ SV4 @ SV4 )
!= SY40 ) )
| ( element @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV5: $i] :
( ( ~ ( element @ SV5 )
| ~ ( ( ( times @ SV5 @ ( sK3_C @ SV5 ) )
!= SV5 )
| ( ( times @ SV5 @ SV5 )
!= ( sK3_C @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV4: $i] :
( ( ( ! [SY40: $i] :
( ( ( times @ SV4 @ SY40 )
!= SV4 )
| ( ( times @ SV4 @ SV4 )
!= SY40 ) ) )
= $true )
| ( ( element @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV5: $i] :
( ( ( ~ ( element @ SV5 ) )
= $true )
| ( ( ~ ( ( ( times @ SV5 @ ( sK3_C @ SV5 ) )
!= SV5 )
| ( ( times @ SV5 @ SV5 )
!= ( sK3_C @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV6: $i,SV4: $i] :
( ( ( ( ( times @ SV4 @ SV6 )
!= SV4 )
| ( ( times @ SV4 @ SV4 )
!= SV6 ) )
= $true )
| ( ( element @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV5: $i] :
( ( ( element @ SV5 )
= $false )
| ( ( ~ ( ( ( times @ SV5 @ ( sK3_C @ SV5 ) )
!= SV5 )
| ( ( times @ SV5 @ SV5 )
!= ( sK3_C @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV6: $i,SV4: $i] :
( ( ( ( ( times @ SV4 @ SV6 )
!= SV4 ) )
= $true )
| ( ( ( ( times @ SV4 @ SV4 )
!= SV6 ) )
= $true )
| ( ( element @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV5: $i] :
( ( ( ( ( times @ SV5 @ ( sK3_C @ SV5 ) )
!= SV5 )
| ( ( times @ SV5 @ SV5 )
!= ( sK3_C @ SV5 ) ) )
= $false )
| ( ( element @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV6: $i,SV4: $i] :
( ( ( ( times @ SV4 @ SV6 )
= SV4 )
= $false )
| ( ( ( ( times @ SV4 @ SV4 )
!= SV6 ) )
= $true )
| ( ( element @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV5: $i] :
( ( ( ( ( times @ SV5 @ ( sK3_C @ SV5 ) )
!= SV5 ) )
= $false )
| ( ( element @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(40,plain,
! [SV5: $i] :
( ( ( ( ( times @ SV5 @ SV5 )
!= ( sK3_C @ SV5 ) ) )
= $false )
| ( ( element @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV6: $i,SV4: $i] :
( ( ( ( times @ SV4 @ SV4 )
= SV6 )
= $false )
| ( ( ( times @ SV4 @ SV6 )
= SV4 )
= $false )
| ( ( element @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV5: $i] :
( ( ( ( times @ SV5 @ ( sK3_C @ SV5 ) )
= SV5 )
= $true )
| ( ( element @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(43,plain,
! [SV5: $i] :
( ( ( ( times @ SV5 @ SV5 )
= ( sK3_C @ SV5 ) )
= $true )
| ( ( element @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV7: $i,SV8: $i,SV9: $i] :
( ( ( times @ ( times @ SV9 @ SV8 ) @ SV7 )
= ( times @ SV8 @ ( times @ SV7 @ SV9 ) ) )
= $true ),
inference(rename,[status(thm)],[27]) ).
thf(48,plain,
! [SV10: $i,SV11: $i] :
( ( ( ( times @ SV11 @ SV11 )
= SV10 )
= $false )
| ( ( ( times @ SV11 @ SV10 )
= SV11 )
= $false )
| ( ( element @ SV11 )
= $true ) ),
inference(rename,[status(thm)],[41]) ).
thf(60,plain,
! [SV12: $i] :
( ( ( ( times @ SV12 @ ( sK3_C @ SV12 ) )
= SV12 )
= $true )
| ( ( element @ SV12 )
= $false ) ),
inference(rename,[status(thm)],[42]) ).
thf(68,plain,
! [SV12: $i] :
( ( ( ( element @ SV12 )
= ( element @ sK1_A ) )
= $false )
| ( ( ( times @ SV12 @ ( sK3_C @ SV12 ) )
= SV12 )
= $true ) ),
inference(res,[status(thm)],[60,18]) ).
thf(69,plain,
! [SV12: $i] :
( ( ( ( element @ SV12 )
= ( element @ sK2_SY36 ) )
= $false )
| ( ( ( times @ SV12 @ ( sK3_C @ SV12 ) )
= SV12 )
= $true ) ),
inference(res,[status(thm)],[60,17]) ).
thf(70,plain,
( ( ( times @ sK2_SY36 @ ( sK3_C @ sK2_SY36 ) )
= sK2_SY36 )
= $true ),
inference(extuni,[status(esa)],[69:[bind(SV12,$thf( sK2_SY36 ))]]) ).
thf(71,plain,
( ( ( times @ sK1_A @ ( sK3_C @ sK1_A ) )
= sK1_A )
= $true ),
inference(extuni,[status(esa)],[68:[bind(SV12,$thf( sK1_A ))]]) ).
thf(72,plain,
! [SV13: $i] :
( ( ( ( times @ SV13 @ SV13 )
= ( sK3_C @ SV13 ) )
= $true )
| ( ( element @ SV13 )
= $false ) ),
inference(rename,[status(thm)],[43]) ).
thf(82,plain,
! [SV13: $i] :
( ( ( ( element @ SV13 )
= ( element @ sK1_A ) )
= $false )
| ( ( ( times @ SV13 @ SV13 )
= ( sK3_C @ SV13 ) )
= $true ) ),
inference(res,[status(thm)],[72,18]) ).
thf(83,plain,
! [SV13: $i] :
( ( ( ( element @ SV13 )
= ( element @ sK2_SY36 ) )
= $false )
| ( ( ( times @ SV13 @ SV13 )
= ( sK3_C @ SV13 ) )
= $true ) ),
inference(res,[status(thm)],[72,17]) ).
thf(84,plain,
( ( ( times @ sK2_SY36 @ sK2_SY36 )
= ( sK3_C @ sK2_SY36 ) )
= $true ),
inference(extuni,[status(esa)],[83:[bind(SV13,$thf( sK2_SY36 ))]]) ).
thf(85,plain,
( ( ( times @ sK1_A @ sK1_A )
= ( sK3_C @ sK1_A ) )
= $true ),
inference(extuni,[status(esa)],[82:[bind(SV13,$thf( sK1_A ))]]) ).
thf(96,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,85,84,72,71,70,60,48,46,22,18]) ).
thf(97,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG210+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 17:19:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 2
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (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)..eprover: CPU time limit exceeded, terminating
% 74.37/74.65 ...eprover: CPU time limit exceeded, terminating
% 149.09/149.40
% 149.09/149.40 (rf:0,axioms:2,ps:2,u:1,ude:false,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)..eprover: CPU time limit exceeded, terminating
% 186.24/186.56 ..eprover: CPU time limit exceeded, terminating
% 223.96/224.27 .
% 223.96/224.27 (rf:0,axioms:2,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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)..eprover: CPU time limit exceeded, terminating
% 262.03/262.46
% 262.03/262.46 (rf:2,axioms:2,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,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)....
% 263.03/263.43
% 263.03/263.43 ********************************
% 263.03/263.43 * All subproblems solved! *
% 263.03/263.43 ********************************
% 263.03/263.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:4,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:148,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:10,foatp_calls:1,translation:fof_full)
% 263.03/263.43
% 263.03/263.43 %**** Beginning of derivation protocol ****
% 263.03/263.43 % SZS output start CNFRefutation
% See solution above
% 263.03/263.43
% 263.03/263.43 %**** End of derivation protocol ****
% 263.03/263.43 %**** no. of clauses in derivation: 57 ****
% 263.03/263.43 %**** clause counter: 96 ****
% 263.03/263.43
% 263.03/263.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:4,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:148,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:10,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------