TSTP Solution File: PUZ062-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : PUZ062-2 : 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 : n024.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 : Mon Jul 18 18:19:33 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 35
% Syntax : Number of formulae : 107 ( 65 unt; 21 typ; 0 def)
% Number of atoms : 334 ( 117 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 1145 ( 57 ~; 68 |; 0 &;1020 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 13 con; 0-4 aty)
% Number of variables : 177 ( 0 ^ 177 !; 0 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_0,type,
c_0: $i ).
thf(tp_c_Finite__Set_OFinites,type,
c_Finite__Set_OFinites: $i ).
thf(tp_c_Finite__Set_Ocard,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(tp_c_Mutil_Ocoloured,type,
c_Mutil_Ocoloured: $i > $i ).
thf(tp_c_Mutil_Odomino,type,
c_Mutil_Odomino: $i ).
thf(tp_c_Mutil_Otiling,type,
c_Mutil_Otiling: $i > $i > $i ).
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_emptyset,type,
c_emptyset: $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_insert,type,
c_insert: $i > $i > $i > $i ).
thf(tp_c_inter,type,
c_inter: $i > $i > $i > $i ).
thf(tp_tc_nat,type,
tc_nat: $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_i,type,
v_i: $i ).
thf(tp_v_j,type,
v_j: $i ).
thf(tp_v_m,type,
v_m: $i ).
thf(tp_v_n,type,
v_n: $i ).
thf(tp_v_t,type,
v_t: $i ).
thf(1,axiom,
! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ c_emptyset @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(2,axiom,
! [V_x: $i,V_A: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(3,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a )
| ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
thf(4,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
thf(5,axiom,
! [V_t: $i] :
( ~ ( c_in @ V_t @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( c_in @ V_t @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).
thf(6,axiom,
! [V_G: $i,T_a: $i,V_F: $i] :
( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
| ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(7,axiom,
! [V_A: $i,T_a: $i,V_x: $i] :
( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
| ( c_in @ V_x @ V_A @ T_a )
| ( ( c_Finite__Set_Ocard @ ( c_insert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Suc @ ( c_Finite__Set_Ocard @ V_A @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
thf(8,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(9,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,negated_conjecture,
( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
!= ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(11,negated_conjecture,
( ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(12,negated_conjecture,
( ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(13,negated_conjecture,
( ( c_inter @ v_a @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(14,negated_conjecture,
( ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(15,negated_conjecture,
c_in @ v_t @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(16,plain,
$false = $false,
inference(unfold_def,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ c_emptyset @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a )
| ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [V_t: $i] :
( ~ ( c_in @ V_t @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( c_in @ V_t @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [V_G: $i,T_a: $i,V_F: $i] :
( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
| ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [V_A: $i,T_a: $i,V_x: $i] :
( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
| ( c_in @ V_x @ V_A @ T_a )
| ( ( c_Finite__Set_Ocard @ ( c_insert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Suc @ ( c_Finite__Set_Ocard @ V_A @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ( ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
!= ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(27,plain,
( ( ( c_inter @ v_a @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) )
= c_emptyset )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(28,plain,
( ( ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(29,plain,
( ( c_in @ v_t @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(32,plain,
( ( ! [V_G: $i,T_a: $i] :
( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
| ! [V_F: $i] : ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(33,plain,
( ( ! [V_A: $i,T_a: $i] :
( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
| ! [V_x: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_insert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Suc @ ( c_Finite__Set_Ocard @ V_A @ T_a ) ) )
| ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(34,plain,
( ( ( ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
!= ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(35,plain,
( ( c_in @ v_t @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(36,plain,
( ( ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(37,plain,
( ( ( c_inter @ v_a @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) )
= c_emptyset )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(38,plain,
( ( ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(39,plain,
( ( ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(40,plain,
( ( ( ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
!= ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(41,plain,
( ( ! [V_A: $i,T_a: $i] :
( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
| ! [V_x: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_insert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Suc @ ( c_Finite__Set_Ocard @ V_A @ T_a ) ) )
| ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(42,plain,
( ( ! [V_G: $i,T_a: $i] :
( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
| ! [V_F: $i] : ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(43,plain,
( ( ! [V_t: $i] :
( ~ ( c_in @ V_t @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( c_in @ V_t @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(44,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(45,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(46,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(47,plain,
( ( ! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ c_emptyset @ T_a ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(48,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(49,plain,
( ( ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV1: $i] :
( ( ! [SY20: $i] :
( ~ ( c_in @ SV1 @ c_Finite__Set_OFinites @ ( tc_set @ SY20 ) )
| ! [SY21: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_insert @ SY21 @ SV1 @ SY20 ) @ SY20 )
= ( c_Suc @ ( c_Finite__Set_Ocard @ SV1 @ SY20 ) ) )
| ( c_in @ SY21 @ SV1 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV2: $i] :
( ( ! [SY22: $i] :
( ~ ( c_in @ SV2 @ c_Finite__Set_OFinites @ ( tc_set @ SY22 ) )
| ! [SY23: $i] : ( c_in @ ( c_inter @ SY23 @ SV2 @ SY22 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV3: $i] :
( ( ~ ( c_in @ SV3 @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( c_in @ SV3 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(53,plain,
! [SV4: $i] :
( ( ! [SY24: $i,SY25: $i,SY26: $i] :
( ~ ( c_in @ SV4 @ ( c_inter @ SY24 @ SY25 @ SY26 ) @ SY26 )
| ( c_in @ SV4 @ SY25 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV5: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ( c_in @ SV5 @ SY27 @ SY28 )
| ! [SY29: $i] :
( ~ ( c_in @ SV5 @ SY29 @ SY28 )
| ( c_in @ SV5 @ ( c_inter @ SY29 @ SY27 @ SY28 ) @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV6: $i] :
( ( ! [SY30: $i,SY31: $i] : ( c_in @ SV6 @ ( c_insert @ SV6 @ SY30 @ SY31 ) @ SY31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV7: $i] :
( ( ! [SY32: $i] :
~ ( c_in @ SV7 @ c_emptyset @ SY32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV8: $i,SV1: $i] :
( ( ~ ( c_in @ SV1 @ c_Finite__Set_OFinites @ ( tc_set @ SV8 ) )
| ! [SY33: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_insert @ SY33 @ SV1 @ SV8 ) @ SV8 )
= ( c_Suc @ ( c_Finite__Set_Ocard @ SV1 @ SV8 ) ) )
| ( c_in @ SY33 @ SV1 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV9: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ c_Finite__Set_OFinites @ ( tc_set @ SV9 ) )
| ! [SY34: $i] : ( c_in @ ( c_inter @ SY34 @ SV2 @ SV9 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(60,plain,
! [SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
= $true )
| ( ( c_in @ SV3 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ~ ( c_in @ SV4 @ ( c_inter @ SV10 @ SY35 @ SY36 ) @ SY36 )
| ( c_in @ SV4 @ SY35 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(62,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY37: $i] :
( ~ ( c_in @ SV5 @ SV11 @ SY37 )
| ! [SY38: $i] :
( ~ ( c_in @ SV5 @ SY38 @ SY37 )
| ( c_in @ SV5 @ ( c_inter @ SY38 @ SV11 @ SY37 ) @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY39: $i] : ( c_in @ SV6 @ ( c_insert @ SV6 @ SV12 @ SY39 ) @ SY39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(64,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( c_in @ SV7 @ c_emptyset @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(65,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ c_Finite__Set_OFinites @ ( tc_set @ SV8 ) ) )
= $true )
| ( ( ! [SY33: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_insert @ SY33 @ SV1 @ SV8 ) @ SV8 )
= ( c_Suc @ ( c_Finite__Set_Ocard @ SV1 @ SV8 ) ) )
| ( c_in @ SY33 @ SV1 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ c_Finite__Set_OFinites @ ( tc_set @ SV9 ) ) )
= $true )
| ( ( ! [SY34: $i] : ( c_in @ ( c_inter @ SY34 @ SV2 @ SV9 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV3: $i] :
( ( ( c_in @ SV3 @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $false )
| ( ( c_in @ SV3 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(68,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ! [SY40: $i] :
( ~ ( c_in @ SV4 @ ( c_inter @ SV10 @ SV14 @ SY40 ) @ SY40 )
| ( c_in @ SV4 @ SV14 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(69,plain,
! [SV15: $i,SV11: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ SV11 @ SV15 )
| ! [SY41: $i] :
( ~ ( c_in @ SV5 @ SY41 @ SV15 )
| ( c_in @ SV5 @ ( c_inter @ SY41 @ SV11 @ SV15 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(70,plain,
! [SV16: $i,SV12: $i,SV6: $i] :
( ( c_in @ SV6 @ ( c_insert @ SV6 @ SV12 @ SV16 ) @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(71,plain,
! [SV13: $i,SV7: $i] :
( ( c_in @ SV7 @ c_emptyset @ SV13 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(72,plain,
! [SV8: $i,SV1: $i] :
( ( ( c_in @ SV1 @ c_Finite__Set_OFinites @ ( tc_set @ SV8 ) )
= $false )
| ( ( ! [SY33: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_insert @ SY33 @ SV1 @ SV8 ) @ SV8 )
= ( c_Suc @ ( c_Finite__Set_Ocard @ SV1 @ SV8 ) ) )
| ( c_in @ SY33 @ SV1 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(73,plain,
! [SV9: $i,SV2: $i] :
( ( ( c_in @ SV2 @ c_Finite__Set_OFinites @ ( tc_set @ SV9 ) )
= $false )
| ( ( ! [SY34: $i] : ( c_in @ ( c_inter @ SY34 @ SV2 @ SV9 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(74,plain,
! [SV17: $i,SV14: $i,SV10: $i,SV4: $i] :
( ( ~ ( c_in @ SV4 @ ( c_inter @ SV10 @ SV14 @ SV17 ) @ SV17 )
| ( c_in @ SV4 @ SV14 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV15: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ SV11 @ SV15 ) )
= $true )
| ( ( ! [SY41: $i] :
( ~ ( c_in @ SV5 @ SY41 @ SV15 )
| ( c_in @ SV5 @ ( c_inter @ SY41 @ SV11 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV8: $i,SV1: $i,SV18: $i] :
( ( ( ( ( c_Finite__Set_Ocard @ ( c_insert @ SV18 @ SV1 @ SV8 ) @ SV8 )
= ( c_Suc @ ( c_Finite__Set_Ocard @ SV1 @ SV8 ) ) )
| ( c_in @ SV18 @ SV1 @ SV8 ) )
= $true )
| ( ( c_in @ SV1 @ c_Finite__Set_OFinites @ ( tc_set @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV9: $i,SV2: $i,SV19: $i] :
( ( ( c_in @ ( c_inter @ SV19 @ SV2 @ SV9 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV9 ) )
= $true )
| ( ( c_in @ SV2 @ c_Finite__Set_OFinites @ ( tc_set @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV17: $i,SV14: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( c_in @ SV4 @ ( c_inter @ SV10 @ SV14 @ SV17 ) @ SV17 ) )
= $true )
| ( ( c_in @ SV4 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV15: $i,SV11: $i,SV5: $i] :
( ( ( c_in @ SV5 @ SV11 @ SV15 )
= $false )
| ( ( ! [SY41: $i] :
( ~ ( c_in @ SV5 @ SY41 @ SV15 )
| ( c_in @ SV5 @ ( c_inter @ SY41 @ SV11 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV8: $i,SV1: $i,SV18: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_insert @ SV18 @ SV1 @ SV8 ) @ SV8 )
= ( c_Suc @ ( c_Finite__Set_Ocard @ SV1 @ SV8 ) ) )
= $true )
| ( ( c_in @ SV18 @ SV1 @ SV8 )
= $true )
| ( ( c_in @ SV1 @ c_Finite__Set_OFinites @ ( tc_set @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV17: $i,SV14: $i,SV10: $i,SV4: $i] :
( ( ( c_in @ SV4 @ ( c_inter @ SV10 @ SV14 @ SV17 ) @ SV17 )
= $false )
| ( ( c_in @ SV4 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV11: $i,SV15: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ SV20 @ SV15 )
| ( c_in @ SV5 @ ( c_inter @ SV20 @ SV11 @ SV15 ) @ SV15 ) )
= $true )
| ( ( c_in @ SV5 @ SV11 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV11: $i,SV15: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ SV20 @ SV15 ) )
= $true )
| ( ( c_in @ SV5 @ ( c_inter @ SV20 @ SV11 @ SV15 ) @ SV15 )
= $true )
| ( ( c_in @ SV5 @ SV11 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(84,plain,
! [SV11: $i,SV15: $i,SV20: $i,SV5: $i] :
( ( ( c_in @ SV5 @ SV20 @ SV15 )
= $false )
| ( ( c_in @ SV5 @ ( c_inter @ SV20 @ SV11 @ SV15 ) @ SV15 )
= $true )
| ( ( c_in @ SV5 @ SV11 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(85,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,84,81,80,77,71,70,67,57,49,39,38,37,36]) ).
thf(86,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ062-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat May 28 22:53:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 13
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:13,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:15,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.20/0.47
% 0.20/0.47 ********************************
% 0.20/0.47 * All subproblems solved! *
% 0.20/0.47 ********************************
% 0.20/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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:85,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.47
% 0.20/0.47 %**** Beginning of derivation protocol ****
% 0.20/0.47 % SZS output start CNFRefutation
% See solution above
% 0.20/0.48
% 0.20/0.48 %**** End of derivation protocol ****
% 0.20/0.48 %**** no. of clauses in derivation: 86 ****
% 0.20/0.48 %**** clause counter: 85 ****
% 0.20/0.48
% 0.20/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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:85,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------