TSTP Solution File: LAT273-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LAT273-2 : 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 : 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 05:45:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of formulae : 76 ( 38 unt; 16 typ; 0 def)
% Number of atoms : 327 ( 82 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1165 ( 73 ~; 103 |; 0 &; 989 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 10 con; 0-4 aty)
% Number of variables : 159 ( 0 ^ 159 !; 0 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Tarski_Ointerval,type,
c_Tarski_Ointerval: $i > $i > $i > $i > $i ).
thf(tp_c_Tarski_OisLub,type,
c_Tarski_OisLub: $i > $i > $i > $i > $o ).
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_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_L,type,
v_L: $i ).
thf(tp_v_S,type,
v_S: $i ).
thf(tp_v_a,type,
v_a: $i ).
thf(tp_v_b,type,
v_b: $i ).
thf(tp_v_cl,type,
v_cl: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_sko__4mi,type,
v_sko__4mi: $i > $i > $i > $i ).
thf(1,axiom,
! [V_S: $i,V_L: $i,V_z: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ~ ( c_in @ V_z @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1) ).
thf(2,axiom,
! [V_S: $i,V_L: $i,V_z: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ~ ( c_in @ V_z @ v_A @ t_a )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_S @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(3,axiom,
! [V_x: $i,V_S: $i,T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(4,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(5,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,negated_conjecture,
~ ( c_in @ ( c_Pair @ v_L @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(7,negated_conjecture,
c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(8,negated_conjecture,
c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,negated_conjecture,
c_in @ v_b @ v_A @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [V_S: $i,V_L: $i,V_z: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ~ ( c_in @ V_z @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [V_S: $i,V_L: $i,V_z: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ~ ( c_in @ V_z @ v_A @ t_a )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_S @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ~ ( c_in @ ( c_Pair @ v_L @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(15,plain,
( ( c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(16,plain,
( ( c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(17,plain,
( ( c_in @ v_b @ v_A @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [V_S: $i,V_L: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ! [V_z: $i] :
( ~ ( c_in @ V_z @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(20,plain,
( ( ! [V_S: $i,V_L: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ! [V_z: $i] :
( ~ ( c_in @ V_z @ v_A @ t_a )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_S @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(21,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(22,plain,
( ( c_in @ v_b @ v_A @ t_a )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(23,plain,
( ( c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
( ( c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(25,plain,
( ( ~ ( c_in @ ( c_Pair @ v_L @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(26,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(27,plain,
( ( ! [V_S: $i,V_L: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ! [V_z: $i] :
( ~ ( c_in @ V_z @ v_A @ t_a )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_S @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(28,plain,
( ( ! [V_S: $i,V_L: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ! [V_z: $i] :
( ~ ( c_in @ V_z @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(29,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(30,plain,
( ( c_in @ ( c_Pair @ v_L @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV1: $i] :
( ( ! [SY12: $i,SY13: $i,SY14: $i] :
( ~ ( c_in @ SV1 @ SY12 @ SY13 )
| ! [SY15: $i,SY16: $i] :
( ~ ( c_lessequals @ SY12 @ ( c_Tarski_Ointerval @ SY14 @ SY15 @ SY16 @ SY13 ) @ ( tc_set @ SY13 ) )
| ( c_in @ ( c_Pair @ SV1 @ SY16 @ SY13 @ SY13 ) @ SY14 @ ( tc_prod @ SY13 @ SY13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV2: $i] :
( ( ! [SY17: $i] :
( ~ ( c_Tarski_OisLub @ SV2 @ v_cl @ SY17 @ t_a )
| ! [SY18: $i] :
( ~ ( c_in @ SY18 @ v_A @ t_a )
| ( c_in @ ( c_Pair @ SY17 @ SY18 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV2 @ v_r @ SY18 ) @ SV2 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV3: $i] :
( ( ! [SY19: $i] :
( ~ ( c_Tarski_OisLub @ SV3 @ v_cl @ SY19 @ t_a )
| ! [SY20: $i] :
( ~ ( c_in @ SY20 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV3 @ v_r @ SY20 ) @ SY20 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SY19 @ SY20 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( c_in @ SV1 @ SV4 @ SY21 )
| ! [SY23: $i,SY24: $i] :
( ~ ( c_lessequals @ SV4 @ ( c_Tarski_Ointerval @ SY22 @ SY23 @ SY24 @ SY21 ) @ ( tc_set @ SY21 ) )
| ( c_in @ ( c_Pair @ SV1 @ SY24 @ SY21 @ SY21 ) @ SY22 @ ( tc_prod @ SY21 @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( c_Tarski_OisLub @ SV2 @ v_cl @ SV5 @ t_a )
| ! [SY25: $i] :
( ~ ( c_in @ SY25 @ v_A @ t_a )
| ( c_in @ ( c_Pair @ SV5 @ SY25 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV2 @ v_r @ SY25 ) @ SV2 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( c_Tarski_OisLub @ SV3 @ v_cl @ SV6 @ t_a )
| ! [SY26: $i] :
( ~ ( c_in @ SY26 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV3 @ v_r @ SY26 ) @ SY26 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV6 @ SY26 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ! [SY27: $i] :
( ~ ( c_in @ SV1 @ SV4 @ SV7 )
| ! [SY28: $i,SY29: $i] :
( ~ ( c_lessequals @ SV4 @ ( c_Tarski_Ointerval @ SY27 @ SY28 @ SY29 @ SV7 ) @ ( tc_set @ SV7 ) )
| ( c_in @ ( c_Pair @ SV1 @ SY29 @ SV7 @ SV7 ) @ SY27 @ ( tc_prod @ SV7 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( c_Tarski_OisLub @ SV2 @ v_cl @ SV5 @ t_a ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( c_in @ SY25 @ v_A @ t_a )
| ( c_in @ ( c_Pair @ SV5 @ SY25 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV2 @ v_r @ SY25 ) @ SV2 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( c_Tarski_OisLub @ SV3 @ v_cl @ SV6 @ t_a ) )
= $true )
| ( ( ! [SY26: $i] :
( ~ ( c_in @ SY26 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV3 @ v_r @ SY26 ) @ SY26 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV6 @ SY26 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV8: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ~ ( c_in @ SV1 @ SV4 @ SV7 )
| ! [SY30: $i,SY31: $i] :
( ~ ( c_lessequals @ SV4 @ ( c_Tarski_Ointerval @ SV8 @ SY30 @ SY31 @ SV7 ) @ ( tc_set @ SV7 ) )
| ( c_in @ ( c_Pair @ SV1 @ SY31 @ SV7 @ SV7 ) @ SV8 @ ( tc_prod @ SV7 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV5: $i,SV2: $i] :
( ( ( c_Tarski_OisLub @ SV2 @ v_cl @ SV5 @ t_a )
= $false )
| ( ( ! [SY25: $i] :
( ~ ( c_in @ SY25 @ v_A @ t_a )
| ( c_in @ ( c_Pair @ SV5 @ SY25 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV2 @ v_r @ SY25 ) @ SV2 @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV6: $i,SV3: $i] :
( ( ( c_Tarski_OisLub @ SV3 @ v_cl @ SV6 @ t_a )
= $false )
| ( ( ! [SY26: $i] :
( ~ ( c_in @ SY26 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV3 @ v_r @ SY26 ) @ SY26 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV6 @ SY26 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV8: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ SV4 @ SV7 ) )
= $true )
| ( ( ! [SY30: $i,SY31: $i] :
( ~ ( c_lessequals @ SV4 @ ( c_Tarski_Ointerval @ SV8 @ SY30 @ SY31 @ SV7 ) @ ( tc_set @ SV7 ) )
| ( c_in @ ( c_Pair @ SV1 @ SY31 @ SV7 @ SV7 ) @ SV8 @ ( tc_prod @ SV7 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV2: $i,SV5: $i,SV9: $i] :
( ( ( ~ ( c_in @ SV9 @ v_A @ t_a )
| ( c_in @ ( c_Pair @ SV5 @ SV9 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV2 @ v_r @ SV9 ) @ SV2 @ t_a ) )
= $true )
| ( ( c_Tarski_OisLub @ SV2 @ v_cl @ SV5 @ t_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV6: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( c_in @ SV10 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV3 @ v_r @ SV10 ) @ SV10 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV6 @ SV10 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_Tarski_OisLub @ SV3 @ v_cl @ SV6 @ t_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV8: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ( c_in @ SV1 @ SV4 @ SV7 )
= $false )
| ( ( ! [SY30: $i,SY31: $i] :
( ~ ( c_lessequals @ SV4 @ ( c_Tarski_Ointerval @ SV8 @ SY30 @ SY31 @ SV7 ) @ ( tc_set @ SV7 ) )
| ( c_in @ ( c_Pair @ SV1 @ SY31 @ SV7 @ SV7 ) @ SV8 @ ( tc_prod @ SV7 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV2: $i,SV5: $i,SV9: $i] :
( ( ( ~ ( c_in @ SV9 @ v_A @ t_a ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV5 @ SV9 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV2 @ v_r @ SV9 ) @ SV2 @ t_a ) )
= $true )
| ( ( c_Tarski_OisLub @ SV2 @ v_cl @ SV5 @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV6: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( c_in @ SV10 @ v_A @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV3 @ v_r @ SV10 ) @ SV10 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV6 @ SV10 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_Tarski_OisLub @ SV3 @ v_cl @ SV6 @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV1: $i,SV7: $i,SV11: $i,SV8: $i,SV4: $i] :
( ( ( ! [SY32: $i] :
( ~ ( c_lessequals @ SV4 @ ( c_Tarski_Ointerval @ SV8 @ SV11 @ SY32 @ SV7 ) @ ( tc_set @ SV7 ) )
| ( c_in @ ( c_Pair @ SV1 @ SY32 @ SV7 @ SV7 ) @ SV8 @ ( tc_prod @ SV7 @ SV7 ) ) ) )
= $true )
| ( ( c_in @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV2: $i,SV5: $i,SV9: $i] :
( ( ( c_in @ SV9 @ v_A @ t_a )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV5 @ SV9 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV2 @ v_r @ SV9 ) @ SV2 @ t_a ) )
= $true )
| ( ( c_Tarski_OisLub @ SV2 @ v_cl @ SV5 @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV6: $i,SV3: $i,SV10: $i] :
( ( ( c_in @ SV10 @ v_A @ t_a )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV3 @ v_r @ SV10 ) @ SV10 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV6 @ SV10 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_Tarski_OisLub @ SV3 @ v_cl @ SV6 @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV1: $i,SV7: $i,SV12: $i,SV11: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( c_lessequals @ SV4 @ ( c_Tarski_Ointerval @ SV8 @ SV11 @ SV12 @ SV7 ) @ ( tc_set @ SV7 ) )
| ( c_in @ ( c_Pair @ SV1 @ SV12 @ SV7 @ SV7 ) @ SV8 @ ( tc_prod @ SV7 @ SV7 ) ) )
= $true )
| ( ( c_in @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV2: $i,SV9: $i,SV5: $i] :
( ( ( c_in @ ( c_Pair @ SV5 @ SV9 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ ( v_sko__4mi @ SV2 @ v_r @ SV9 ) @ SV2 @ t_a )
= $true )
| ( ( c_in @ SV9 @ v_A @ t_a )
= $false )
| ( ( c_Tarski_OisLub @ SV2 @ v_cl @ SV5 @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV6: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV3 @ v_r @ SV10 ) @ SV10 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV6 @ SV10 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ SV10 @ v_A @ t_a )
= $false )
| ( ( c_Tarski_OisLub @ SV3 @ v_cl @ SV6 @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV1: $i,SV7: $i,SV12: $i,SV11: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( c_lessequals @ SV4 @ ( c_Tarski_Ointerval @ SV8 @ SV11 @ SV12 @ SV7 ) @ ( tc_set @ SV7 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1 @ SV12 @ SV7 @ SV7 ) @ SV8 @ ( tc_prod @ SV7 @ SV7 ) )
= $true )
| ( ( c_in @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV6: $i,SV10: $i,SV3: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV3 @ v_r @ SV10 ) @ SV10 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV6 @ SV10 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ SV10 @ v_A @ t_a )
= $false )
| ( ( c_Tarski_OisLub @ SV3 @ v_cl @ SV6 @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV1: $i,SV7: $i,SV12: $i,SV11: $i,SV8: $i,SV4: $i] :
( ( ( c_lessequals @ SV4 @ ( c_Tarski_Ointerval @ SV8 @ SV11 @ SV12 @ SV7 ) @ ( tc_set @ SV7 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1 @ SV12 @ SV7 @ SV7 ) @ SV8 @ ( tc_prod @ SV7 @ SV7 ) )
= $true )
| ( ( c_in @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,58,57,54,34,30,24,23]) ).
thf(60,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT273-2 : 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 : n004.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 17:17:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 7
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.19/0.36 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:9,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.19/0.43
% 0.19/0.43 ********************************
% 0.19/0.43 * All subproblems solved! *
% 0.19/0.43 ********************************
% 0.19/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox/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:59,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.43
% 0.19/0.43 %**** Beginning of derivation protocol ****
% 0.19/0.43 % SZS output start CNFRefutation
% See solution above
% 0.19/0.43
% 0.19/0.43 %**** End of derivation protocol ****
% 0.19/0.43 %**** no. of clauses in derivation: 60 ****
% 0.19/0.43 %**** clause counter: 59 ****
% 0.19/0.43
% 0.19/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox/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:59,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------