TSTP Solution File: LAT268-10 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LAT268-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n004.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 05:45:21 EDT 2022
% Result : Unsatisfiable 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 35
% Syntax : Number of formulae : 84 ( 62 unt; 22 typ; 0 def)
% Number of atoms : 158 ( 102 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 826 ( 6 ~; 0 |; 0 &; 820 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 12 con; 0-4 aty)
% Number of variables : 102 ( 0 ^ 102 !; 0 ?; 102 :)
% 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 > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $i ).
thf(tp_ifeq,type,
ifeq: $i > $i > $i > $i > $i ).
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_true,type,
true: $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 ) )
= true ),
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 ) )
= true ),
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] :
( ( ifeq @ ( 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 ) ) @ true @ ( 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 )
= true ),
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_S: $i,V_cl: $i,T_a: $i,V_x: $i] :
( ( ifeq @ ( c_lessequals @ V_S @ ( c_Tarski_Opotype_Opset @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_set @ T_a ) ) @ true @ ( ifeq @ ( c_in @ V_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ V_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ V_x @ V_S @ T_a ) @ true @ ( 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 ) @ true ) @ true ) @ true )
= true ),
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,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(10,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(11,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,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 ) )
!= true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(13,negated_conjecture,
( ( c_in @ v_x @ v_S @ t_a )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(14,negated_conjecture,
( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(15,plain,
$false = $false,
inference(unfold_def,[status(thm)],[11]) ).
thf(16,plain,
( ( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,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(18,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(19,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 )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,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 )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_cl: $i] :
( ( ifeq @ ( 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 ) ) @ true @ ( 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 )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ! [V_S: $i,V_cl: $i,T_a: $i,V_x: $i] :
( ( ifeq @ ( c_lessequals @ V_S @ ( c_Tarski_Opotype_Opset @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_set @ T_a ) ) @ true @ ( ifeq @ ( c_in @ V_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ V_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ V_x @ V_S @ T_a ) @ true @ ( 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 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(23,plain,
( ( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,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 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(26,plain,
( ( ( c_in @ v_x @ v_S @ t_a )
= true )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(27,plain,
( ( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
= true )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,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 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(30,plain,
( ( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
= true )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(31,plain,
( ( ( c_in @ v_x @ v_S @ t_a )
= true )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(32,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 ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(33,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(34,plain,
( ( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(35,plain,
( ( ! [V_S: $i,V_cl: $i,T_a: $i,V_x: $i] :
( ( ifeq @ ( c_lessequals @ V_S @ ( c_Tarski_Opotype_Opset @ V_cl @ T_a @ tc_Product__Type_Ounit ) @ ( tc_set @ T_a ) ) @ true @ ( ifeq @ ( c_in @ V_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ V_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ V_x @ V_S @ T_a ) @ true @ ( 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 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(36,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_cl: $i] :
( ( ifeq @ ( 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 ) ) @ true @ ( 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 )
= true ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(37,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 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(38,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 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(39,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)],[18]) ).
thf(40,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)],[17]) ).
thf(41,plain,
( ( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(42,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,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 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(44,plain,
! [SV1: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ( ifeq @ SV1 @ SV1 @ SY16 @ SY17 )
= SY16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(45,plain,
! [SV2: $i] :
( ( ! [SY18: $i,SY19: $i,SY20: $i] :
( ( ifeq @ ( c_lessequals @ SV2 @ ( c_Tarski_Opotype_Opset @ SY18 @ SY19 @ tc_Product__Type_Ounit ) @ ( tc_set @ SY19 ) ) @ true @ ( ifeq @ ( c_in @ SY18 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SY19 @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ SY18 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SY19 @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ SY20 @ SV2 @ SY19 ) @ true @ ( c_in @ ( c_Pair @ SY20 @ ( c_Tarski_Olub @ SV2 @ SY18 @ SY19 ) @ SY19 @ SY19 ) @ ( c_Tarski_Opotype_Oorder @ SY18 @ SY19 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY19 @ SY19 ) ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(46,plain,
! [SV3: $i] :
( ( ! [SY21: $i,SY22: $i,SY23: $i] :
( ( ifeq @ ( c_in @ ( c_Pair @ SV3 @ SY21 @ SY22 @ SY22 ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ SY23 @ SY22 ) @ SY22 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY22 @ SY22 ) ) @ true @ ( c_in @ ( c_Pair @ SY21 @ SV3 @ SY22 @ SY22 ) @ ( c_Tarski_Opotype_Oorder @ SY23 @ SY22 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY22 @ SY22 ) ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(47,plain,
! [SV4: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ( c_Tarski_Oglb @ SV4 @ SY24 @ SY25 )
= ( c_Tarski_Olub @ SV4 @ ( c_Tarski_Odual @ SY24 @ SY25 ) @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV5: $i] :
( ( ! [SY26: $i] :
( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ SV5 @ SY26 ) @ SY26 @ tc_Product__Type_Ounit )
= ( c_Tarski_Opotype_Opset @ SV5 @ SY26 @ tc_Product__Type_Ounit ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY27: $i] :
( ( ifeq @ SV1 @ SV1 @ SV6 @ SY27 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ( ifeq @ ( c_lessequals @ SV2 @ ( c_Tarski_Opotype_Opset @ SV7 @ SY28 @ tc_Product__Type_Ounit ) @ ( tc_set @ SY28 ) ) @ true @ ( ifeq @ ( c_in @ SV7 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SY28 @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ SV7 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SY28 @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ SY29 @ SV2 @ SY28 ) @ true @ ( c_in @ ( c_Pair @ SY29 @ ( c_Tarski_Olub @ SV2 @ SV7 @ SY28 ) @ SY28 @ SY28 ) @ ( c_Tarski_Opotype_Oorder @ SV7 @ SY28 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY28 @ SY28 ) ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ( ifeq @ ( c_in @ ( c_Pair @ SV3 @ SV8 @ SY30 @ SY30 ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ SY31 @ SY30 ) @ SY30 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY30 @ SY30 ) ) @ true @ ( c_in @ ( c_Pair @ SV8 @ SV3 @ SY30 @ SY30 ) @ ( c_Tarski_Opotype_Oorder @ SY31 @ SY30 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SY30 @ SY30 ) ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY32: $i] :
( ( c_Tarski_Oglb @ SV4 @ SV9 @ SY32 )
= ( c_Tarski_Olub @ SV4 @ ( c_Tarski_Odual @ SV9 @ SY32 ) @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV10: $i,SV5: $i] :
( ( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ SV5 @ SV10 ) @ SV10 @ tc_Product__Type_Ounit )
= ( c_Tarski_Opotype_Opset @ SV5 @ SV10 @ tc_Product__Type_Ounit ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( ifeq @ SV1 @ SV1 @ SV6 @ SV11 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ! [SY33: $i] :
( ( ifeq @ ( c_lessequals @ SV2 @ ( c_Tarski_Opotype_Opset @ SV7 @ SV12 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV12 ) ) @ true @ ( ifeq @ ( c_in @ SV7 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV12 @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ SV7 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV12 @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ SY33 @ SV2 @ SV12 ) @ true @ ( c_in @ ( c_Pair @ SY33 @ ( c_Tarski_Olub @ SV2 @ SV7 @ SV12 ) @ SV12 @ SV12 ) @ ( c_Tarski_Opotype_Oorder @ SV7 @ SV12 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV12 @ SV12 ) ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ! [SY34: $i] :
( ( ifeq @ ( c_in @ ( c_Pair @ SV3 @ SV8 @ SV13 @ SV13 ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ SY34 @ SV13 ) @ SV13 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV13 @ SV13 ) ) @ true @ ( c_in @ ( c_Pair @ SV8 @ SV3 @ SV13 @ SV13 ) @ ( c_Tarski_Opotype_Oorder @ SY34 @ SV13 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV13 @ SV13 ) ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV14: $i,SV9: $i,SV4: $i] :
( ( ( c_Tarski_Oglb @ SV4 @ SV9 @ SV14 )
= ( c_Tarski_Olub @ SV4 @ ( c_Tarski_Odual @ SV9 @ SV14 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV15: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( ifeq @ ( c_lessequals @ SV2 @ ( c_Tarski_Opotype_Opset @ SV7 @ SV12 @ tc_Product__Type_Ounit ) @ ( tc_set @ SV12 ) ) @ true @ ( ifeq @ ( c_in @ SV7 @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV12 @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ SV7 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV12 @ tc_Product__Type_Ounit ) ) @ true @ ( ifeq @ ( c_in @ SV15 @ SV2 @ SV12 ) @ true @ ( c_in @ ( c_Pair @ SV15 @ ( c_Tarski_Olub @ SV2 @ SV7 @ SV12 ) @ SV12 @ SV12 ) @ ( c_Tarski_Opotype_Oorder @ SV7 @ SV12 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV12 @ SV12 ) ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV16: $i,SV13: $i,SV8: $i,SV3: $i] :
( ( ( ifeq @ ( c_in @ ( c_Pair @ SV3 @ SV8 @ SV13 @ SV13 ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ SV16 @ SV13 ) @ SV13 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV13 @ SV13 ) ) @ true @ ( c_in @ ( c_Pair @ SV8 @ SV3 @ SV13 @ SV13 ) @ ( c_Tarski_Opotype_Oorder @ SV16 @ SV13 @ tc_Product__Type_Ounit ) @ ( tc_prod @ SV13 @ SV13 ) ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,60,59,58,55,54,49,43,41,38,37,34,31]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT268-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n004.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 29 19:33:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36
% 0.12/0.36 No.of.Axioms: 12
% 0.12/0.36
% 0.12/0.36 Length.of.Defs: 0
% 0.12/0.36
% 0.12/0.36 Contains.Choice.Funs: false
% 0.18/0.37 (rf:0,axioms:12,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:14,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.18/0.50
% 0.18/0.50 ********************************
% 0.18/0.50 * All subproblems solved! *
% 0.18/0.50 ********************************
% 0.18/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.50
% 0.18/0.50 %**** Beginning of derivation protocol ****
% 0.18/0.50 % SZS output start CNFRefutation
% See solution above
% 0.18/0.50
% 0.18/0.50 %**** End of derivation protocol ****
% 0.18/0.50 %**** no. of clauses in derivation: 62 ****
% 0.18/0.50 %**** clause counter: 61 ****
% 0.18/0.50
% 0.18/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------