TSTP Solution File: SEU167+3 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n011.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 12:07:31 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 48 unt; 9 typ; 0 def)
% Number of atoms : 262 ( 67 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 507 ( 49 ~; 43 |; 13 &; 391 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 129 ( 0 ^ 125 !; 4 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_SY19,type,
sK4_SY19: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(3,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(7,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY14: $i,SY15: $i,SY16: $i] :
( ( ( subset @ sK1_A @ SY14 )
& ( subset @ SY15 @ SY16 ) )
=> ( subset @ ( cartesian_product2 @ sK1_A @ SY15 ) @ ( cartesian_product2 @ SY14 @ SY16 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ! [SY17: $i,SY18: $i] :
( ( ( subset @ sK1_A @ sK2_SY14 )
& ( subset @ SY17 @ SY18 ) )
=> ( subset @ ( cartesian_product2 @ sK1_A @ SY17 ) @ ( cartesian_product2 @ sK2_SY14 @ SY18 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [SY19: $i] :
( ( ( subset @ sK1_A @ sK2_SY14 )
& ( subset @ sK3_SY17 @ SY19 ) )
=> ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY17 ) @ ( cartesian_product2 @ sK2_SY14 @ SY19 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( ( ( subset @ sK1_A @ sK2_SY14 )
& ( subset @ sK3_SY17 @ sK4_SY19 ) )
=> ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY17 ) @ ( cartesian_product2 @ sK2_SY14 @ sK4_SY19 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( subset @ sK1_A @ sK2_SY14 )
= $true ),
inference(standard_cnf,[status(thm)],[17]) ).
thf(19,plain,
( ( subset @ sK3_SY17 @ sK4_SY19 )
= $true ),
inference(standard_cnf,[status(thm)],[17]) ).
thf(20,plain,
( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY17 ) @ ( cartesian_product2 @ sK2_SY14 @ sK4_SY19 ) )
= $false ),
inference(standard_cnf,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY17 ) @ ( cartesian_product2 @ sK2_SY14 @ sK4_SY19 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(23,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(24,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(25,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(26,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(27,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(28,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(29,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(30,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(32,plain,
( ( subset @ sK3_SY17 @ sK4_SY19 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(33,plain,
( ( subset @ sK1_A @ sK2_SY14 )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(34,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY17 ) @ ( cartesian_product2 @ sK2_SY14 @ sK4_SY19 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(35,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(36,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
! [SV2: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ~ ( subset @ SV2 @ SY20 )
| ~ ( subset @ SY20 @ SY21 )
| ( subset @ SV2 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY17 ) @ ( cartesian_product2 @ sK2_SY14 @ sK4_SY19 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY22: $i] :
( ~ ( subset @ SV3 @ SY22 )
| ! [SY23: $i] : ( subset @ ( cartesian_product2 @ SV3 @ SY23 ) @ ( cartesian_product2 @ SY22 @ SY23 ) ) )
| ~ ! [SY24: $i] :
( ~ ( subset @ SV3 @ SY24 )
| ! [SY25: $i] : ( subset @ ( cartesian_product2 @ SY25 @ SV3 ) @ ( cartesian_product2 @ SY25 @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY26: $i] :
( ~ ( subset @ SV2 @ SV4 )
| ~ ( subset @ SV4 @ SY26 )
| ( subset @ SV2 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV3: $i] :
( ( ~ ! [SY22: $i] :
( ~ ( subset @ SV3 @ SY22 )
| ! [SY23: $i] : ( subset @ ( cartesian_product2 @ SV3 @ SY23 ) @ ( cartesian_product2 @ SY22 @ SY23 ) ) )
| ~ ! [SY24: $i] :
( ~ ( subset @ SV3 @ SY24 )
| ! [SY25: $i] : ( subset @ ( cartesian_product2 @ SY25 @ SV3 ) @ ( cartesian_product2 @ SY25 @ SY24 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV4 )
| ~ ( subset @ SV4 @ SV5 )
| ( subset @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV3: $i] :
( ( ~ ! [SY22: $i] :
( ~ ( subset @ SV3 @ SY22 )
| ! [SY23: $i] : ( subset @ ( cartesian_product2 @ SV3 @ SY23 ) @ ( cartesian_product2 @ SY22 @ SY23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(45,plain,
! [SV3: $i] :
( ( ~ ! [SY24: $i] :
( ~ ( subset @ SV3 @ SY24 )
| ! [SY25: $i] : ( subset @ ( cartesian_product2 @ SY25 @ SV3 ) @ ( cartesian_product2 @ SY25 @ SY24 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV4 )
| ~ ( subset @ SV4 @ SV5 ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
( ~ ( subset @ SV3 @ SY22 )
| ! [SY23: $i] : ( subset @ ( cartesian_product2 @ SV3 @ SY23 ) @ ( cartesian_product2 @ SY22 @ SY23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV3: $i] :
( ( ! [SY24: $i] :
( ~ ( subset @ SV3 @ SY24 )
| ! [SY25: $i] : ( subset @ ( cartesian_product2 @ SY25 @ SV3 ) @ ( cartesian_product2 @ SY25 @ SY24 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(49,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ( subset @ SV4 @ SV5 ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV6 )
| ! [SY27: $i] : ( subset @ ( cartesian_product2 @ SV3 @ SY27 ) @ ( cartesian_product2 @ SV6 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV7 )
| ! [SY28: $i] : ( subset @ ( cartesian_product2 @ SY28 @ SV3 ) @ ( cartesian_product2 @ SY28 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV4 )
= $false )
| ( ( ~ ( subset @ SV4 @ SV5 ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY27: $i] : ( subset @ ( cartesian_product2 @ SV3 @ SY27 ) @ ( cartesian_product2 @ SV6 @ SY27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV7 ) )
= $true )
| ( ( ! [SY28: $i] : ( subset @ ( cartesian_product2 @ SY28 @ SV3 ) @ ( cartesian_product2 @ SY28 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV2: $i,SV5: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV5 )
= $false )
| ( ( subset @ SV2 @ SV4 )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV6: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV6 )
= $false )
| ( ( ! [SY27: $i] : ( subset @ ( cartesian_product2 @ SV3 @ SY27 ) @ ( cartesian_product2 @ SV6 @ SY27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV7: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV7 )
= $false )
| ( ( ! [SY28: $i] : ( subset @ ( cartesian_product2 @ SY28 @ SV3 ) @ ( cartesian_product2 @ SY28 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( subset @ ( cartesian_product2 @ SV3 @ SV8 ) @ ( cartesian_product2 @ SV6 @ SV8 ) )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ( subset @ ( cartesian_product2 @ SV9 @ SV3 ) @ ( cartesian_product2 @ SV9 @ SV7 ) )
= $true )
| ( ( subset @ SV3 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,59,58,55,39,37,36,33,32]) ).
thf(61,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 07:07:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 5
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.19/0.35 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:7,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/sandbox2/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:60,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: 61 ****
% 0.19/0.39 %**** clause counter: 60 ****
% 0.19/0.39
% 0.19/0.39 % SZS status Theorem for /export/starexec/sandbox2/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:60,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------