TSTP Solution File: LAT268-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LAT268-2 : 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 : n018.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 : Sun Jul 17 05:45:22 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 32
% Syntax : Number of formulae : 86 ( 53 unt; 20 typ; 0 def)
% Number of atoms : 291 ( 93 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 1144 ( 60 ~; 73 |; 0 &;1011 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 11 con; 0-4 aty)
% Number of variables : 128 ( 0 ^ 128 !; 0 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Tarski_OCompleteLattice,type,
c_Tarski_OCompleteLattice: $i ).
thf(tp_c_Tarski_OPartialOrder,type,
c_Tarski_OPartialOrder: $i ).
thf(tp_c_Tarski_Odual,type,
c_Tarski_Odual: $i > $i > $i ).
thf(tp_c_Tarski_Oglb,type,
c_Tarski_Oglb: $i > $i > $i > $i ).
thf(tp_c_Tarski_Olub,type,
c_Tarski_Olub: $i > $i > $i > $i ).
thf(tp_c_Tarski_Opotype_Oorder,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(tp_c_Tarski_Opotype_Opset,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
thf(tp_tc_Tarski_Opotype_Opotype__ext__type,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_A,type,
v_A: $i ).
thf(tp_v_S,type,
v_S: $i ).
thf(tp_v_cl,type,
v_cl: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(1,axiom,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(2,axiom,
! [V_cl: $i,T_a: $i] :
( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ V_cl @ T_a ) @ T_a @ tc_Product__Type_Ounit )
= ( c_Tarski_Opotype_Opset @ V_cl @ T_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
thf(3,axiom,
! [V_S: $i,V_cl: $i,T_a: $i] :
( ( c_Tarski_Oglb @ V_S @ V_cl @ T_a )
= ( c_Tarski_Olub @ V_S @ ( c_Tarski_Odual @ V_cl @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
thf(4,axiom,
c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
thf(5,axiom,
c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
thf(6,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_cl: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ V_cl @ T_a ) @ T_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Tarski_Opotype_Oorder @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) ).
thf(7,axiom,
! [V_x: $i,V_S: $i,T_a: $i,V_cl: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ~ ( c_in @ V_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ V_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Opotype_Opset @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ ( c_Tarski_Olub @ V_S @ V_cl @ T_a ) @ T_a @ T_a ) @ ( c_Tarski_Opotype_Oorder @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
thf(8,axiom,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
~ ( c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(12,negated_conjecture,
c_in @ v_x @ v_S @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(13,negated_conjecture,
c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(14,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(15,plain,
( ( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [V_cl: $i,T_a: $i] :
( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ V_cl @ T_a ) @ T_a @ tc_Product__Type_Ounit )
= ( c_Tarski_Opotype_Opset @ V_cl @ T_a @ tc_Product__Type_Ounit ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [V_S: $i,V_cl: $i,T_a: $i] :
( ( c_Tarski_Oglb @ V_S @ V_cl @ T_a )
= ( c_Tarski_Olub @ V_S @ ( c_Tarski_Odual @ V_cl @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_cl: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ V_cl @ T_a ) @ T_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Tarski_Opotype_Oorder @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i,V_cl: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ~ ( c_in @ V_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ V_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Opotype_Opset @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ ( c_Tarski_Olub @ V_S @ V_cl @ T_a ) @ T_a @ T_a ) @ ( c_Tarski_Opotype_Oorder @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(24,plain,
( ( c_in @ v_x @ v_S @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(25,plain,
( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(26,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ! [V_cl: $i] :
( ~ ( c_in @ V_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ V_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Opotype_Opset @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ ( c_Tarski_Olub @ V_S @ V_cl @ T_a ) @ T_a @ T_a ) @ ( c_Tarski_Opotype_Oorder @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(28,plain,
( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(29,plain,
( ( c_in @ v_x @ v_S @ t_a )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(30,plain,
( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(31,plain,
( ( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(32,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ! [V_cl: $i] :
( ~ ( c_in @ V_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ V_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Opotype_Opset @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ ( c_Tarski_Olub @ V_S @ V_cl @ T_a ) @ T_a @ T_a ) @ ( c_Tarski_Opotype_Oorder @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(33,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_cl: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ V_cl @ T_a ) @ T_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Tarski_Opotype_Oorder @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(34,plain,
( ( c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(35,plain,
( ( c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(36,plain,
( ( ! [V_S: $i,V_cl: $i,T_a: $i] :
( ( c_Tarski_Oglb @ V_S @ V_cl @ T_a )
= ( c_Tarski_Olub @ V_S @ ( c_Tarski_Odual @ V_cl @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(37,plain,
( ( ! [V_cl: $i,T_a: $i] :
( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ V_cl @ T_a ) @ T_a @ tc_Product__Type_Ounit )
= ( c_Tarski_Opotype_Opset @ V_cl @ T_a @ tc_Product__Type_Ounit ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(38,plain,
( ( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(39,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV1: $i] :
( ( ! [SY13: $i,SY14: $i] :
( ~ ( c_in @ SV1 @ SY13 @ SY14 )
| ! [SY15: $i] :
( ~ ( c_in @ SY15 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SY14 @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ SY15 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SY14 @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ SY13 @ ( c_Tarski_Opotype_Opset @ SY15 @ SY14 @ tc_Product__Type_Ounit ) @ ( tc_set @ SY14 ) )
| ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SY13 @ SY15 @ SY14 ) @ SY14 @ SY14 ) @ ( c_Tarski_Opotype_Oorder @ SY15 @ SY14 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY14 @ SY14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV2: $i] :
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ~ ( c_in @ ( c_Pair @ SV2 @ SY16 @ SY17 @ SY17 ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ SY18 @ SY17 ) @ SY17 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY17 @ SY17 ) )
| ( c_in @ ( c_Pair @ SY16 @ SV2 @ SY17 @ SY17 ) @ ( c_Tarski_Opotype_Oorder @ SY18 @ SY17 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY17 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(43,plain,
! [SV3: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ( c_Tarski_Oglb @ SV3 @ SY19 @ SY20 )
= ( c_Tarski_Olub @ SV3 @ ( c_Tarski_Odual @ SY19 @ SY20 ) @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV4: $i] :
( ( ! [SY21: $i] :
( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ SV4 @ SY21 ) @ SY21 @ tc_Product__Type_Ounit )
= ( c_Tarski_Opotype_Opset @ SV4 @ SY21 @ tc_Product__Type_Ounit ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY22: $i] :
( ~ ( c_in @ SV1 @ SV5 @ SY22 )
| ! [SY23: $i] :
( ~ ( c_in @ SY23 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SY22 @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ SY23 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SY22 @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SY23 @ SY22 @ tc_Product__Type_Ounit ) @ ( tc_set @ SY22 ) )
| ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SY23 @ SY22 ) @ SY22 @ SY22 ) @ ( c_Tarski_Opotype_Oorder @ SY23 @ SY22 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY22 @ SY22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ~ ( c_in @ ( c_Pair @ SV2 @ SV6 @ SY24 @ SY24 ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ SY25 @ SY24 ) @ SY24 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY24 @ SY24 ) )
| ( c_in @ ( c_Pair @ SV6 @ SV2 @ SY24 @ SY24 ) @ ( c_Tarski_Opotype_Oorder @ SY25 @ SY24 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY24 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY26: $i] :
( ( c_Tarski_Oglb @ SV3 @ SV7 @ SY26 )
= ( c_Tarski_Olub @ SV3 @ ( c_Tarski_Odual @ SV7 @ SY26 ) @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV8: $i,SV4: $i] :
( ( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ SV4 @ SV8 ) @ SV8 @ tc_Product__Type_Ounit )
= ( c_Tarski_Opotype_Opset @ SV4 @ SV8 @ tc_Product__Type_Ounit ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ~ ( c_in @ SV1 @ SV5 @ SV9 )
| ! [SY27: $i] :
( ~ ( c_in @ SY27 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ SY27 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SY27 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV9 ) )
| ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SY27 @ SV9 ) @ SV9 @ SV9 ) @ ( c_Tarski_Opotype_Oorder @ SY27 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV9 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ! [SY28: $i] :
( ~ ( c_in @ ( c_Pair @ SV2 @ SV6 @ SV10 @ SV10 ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ SY28 @ SV10 ) @ SV10 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV10 @ SV10 ) )
| ( c_in @ ( c_Pair @ SV6 @ SV2 @ SV10 @ SV10 ) @ ( c_Tarski_Opotype_Oorder @ SY28 @ SV10 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV10 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV11: $i,SV7: $i,SV3: $i] :
( ( ( c_Tarski_Oglb @ SV3 @ SV7 @ SV11 )
= ( c_Tarski_Olub @ SV3 @ ( c_Tarski_Odual @ SV7 @ SV11 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ SV5 @ SV9 ) )
= $true )
| ( ( ! [SY27: $i] :
( ~ ( c_in @ SY27 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ SY27 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SY27 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV9 ) )
| ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SY27 @ SV9 ) @ SV9 @ SV9 ) @ ( c_Tarski_Opotype_Oorder @ SY27 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV9 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV12: $i,SV10: $i,SV6: $i,SV2: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV2 @ SV6 @ SV10 @ SV10 ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ SV12 @ SV10 ) @ SV10 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV10 @ SV10 ) )
| ( c_in @ ( c_Pair @ SV6 @ SV2 @ SV10 @ SV10 ) @ ( c_Tarski_Opotype_Oorder @ SV12 @ SV10 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV10 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( c_in @ SV1 @ SV5 @ SV9 )
= $false )
| ( ( ! [SY27: $i] :
( ~ ( c_in @ SY27 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ SY27 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SY27 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV9 ) )
| ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SY27 @ SV9 ) @ SV9 @ SV9 ) @ ( c_Tarski_Opotype_Oorder @ SY27 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV9 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV12: $i,SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2 @ SV6 @ SV10 @ SV10 ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ SV12 @ SV10 ) @ SV10 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV10 @ SV10 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV6 @ SV2 @ SV10 @ SV10 ) @ ( c_Tarski_Opotype_Oorder @ SV12 @ SV10 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV10 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV1: $i,SV5: $i,SV9: $i,SV13: $i] :
( ( ( ~ ( c_in @ SV13 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ SV13 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV9 ) )
| ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SV13 @ SV9 ) @ SV9 @ SV9 ) @ ( c_Tarski_Opotype_Oorder @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV9 @ SV9 ) ) )
= $true )
| ( ( c_in @ SV1 @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV12: $i,SV10: $i,SV6: $i,SV2: $i] :
( ( ( c_in @ ( c_Pair @ SV2 @ SV6 @ SV10 @ SV10 ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ SV12 @ SV10 ) @ SV10 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV10 @ SV10 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV6 @ SV2 @ SV10 @ SV10 ) @ ( c_Tarski_Opotype_Oorder @ SV12 @ SV10 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV10 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV1: $i,SV5: $i,SV9: $i,SV13: $i] :
( ( ( ~ ( c_in @ SV13 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) ) )
= $true )
| ( ( ~ ( c_in @ SV13 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV9 ) )
| ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SV13 @ SV9 ) @ SV9 @ SV9 ) @ ( c_Tarski_Opotype_Oorder @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV9 @ SV9 ) ) )
= $true )
| ( ( c_in @ SV1 @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV1: $i,SV5: $i,SV9: $i,SV13: $i] :
( ( ( c_in @ SV13 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
= $false )
| ( ( ~ ( c_in @ SV13 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV9 ) )
| ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SV13 @ SV9 ) @ SV9 @ SV9 ) @ ( c_Tarski_Opotype_Oorder @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV9 @ SV9 ) ) )
= $true )
| ( ( c_in @ SV1 @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(61,plain,
! [SV1: $i,SV5: $i,SV9: $i,SV13: $i] :
( ( ( ~ ( c_in @ SV13 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV9 ) )
| ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SV13 @ SV9 ) @ SV9 @ SV9 ) @ ( c_Tarski_Opotype_Oorder @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV9 @ SV9 ) ) )
= $true )
| ( ( c_in @ SV13 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
= $false )
| ( ( c_in @ SV1 @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(62,plain,
! [SV1: $i,SV5: $i,SV9: $i,SV13: $i] :
( ( ( c_in @ SV13 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
= $false )
| ( ( ~ ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV9 ) )
| ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SV13 @ SV9 ) @ SV9 @ SV9 ) @ ( c_Tarski_Opotype_Oorder @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV9 @ SV9 ) ) )
= $true )
| ( ( c_in @ SV13 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
= $false )
| ( ( c_in @ SV1 @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(63,plain,
! [SV1: $i,SV9: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV9 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SV13 @ SV9 ) @ SV9 @ SV9 ) @ ( c_Tarski_Opotype_Oorder @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV9 @ SV9 ) )
= $true )
| ( ( c_in @ SV13 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
= $false )
| ( ( c_in @ SV13 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
= $false )
| ( ( c_in @ SV1 @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(64,plain,
! [SV1: $i,SV9: $i,SV13: $i,SV5: $i] :
( ( ( c_lessequals @ SV5 @ ( c_Tarski_Opotype_Opset @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV9 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1 @ ( c_Tarski_Olub @ SV5 @ SV13 @ SV9 ) @ SV9 @ SV9 ) @ ( c_Tarski_Opotype_Oorder @ SV13 @ SV9 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV9 @ SV9 ) )
= $true )
| ( ( c_in @ SV13 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
= $false )
| ( ( c_in @ SV13 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV9 @ tc_Product__Type_Ounit ) )
= $false )
| ( ( c_in @ SV1 @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(65,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,64,58,52,49,45,40,38,35,34,31,29]) ).
thf(66,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT268-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n018.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 : Wed Jun 29 00:21:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 11
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.36 (rf:0,axioms:11,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:13,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.19/0.46
% 0.19/0.46 ********************************
% 0.19/0.46 * All subproblems solved! *
% 0.19/0.46 ********************************
% 0.19/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,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:65,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.46
% 0.19/0.46 %**** Beginning of derivation protocol ****
% 0.19/0.46 % SZS output start CNFRefutation
% See solution above
% 0.19/0.46
% 0.19/0.46 %**** End of derivation protocol ****
% 0.19/0.46 %**** no. of clauses in derivation: 66 ****
% 0.19/0.46 %**** clause counter: 65 ****
% 0.19/0.46
% 0.19/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,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:65,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------